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Paper Citation Record · LEDGER

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations

As of 21 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 0 inbound Pith citation observations for arXiv:2508.18840.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2508.18840 v1

Coverage vector

measured 49 of 49 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T16:23:06.616618Z

measured 49 of 49 standing notices

One-hop event checks from named stored sources.

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measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

49 of 49 outbound references displayed

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External citation measurements

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Outbound references

Observation 5b950f86-c373-45e4-8355-5b21f34ec201 · outbound

This paper cites Alves, C.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Alves, C

Reference 1

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Source-reported events for the cited work

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Observation 4b7c44c8-ac52-4b7e-a70c-cb42550e7388 · outbound

This paper cites Alves, C.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Alves, C

Reference 2

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Observation cd18ab5b-eb34-4d88-8a87-6d39f164998c · outbound

This paper cites Ambrosio, Concentration phenomena for a class of fractional Kirchhoff equations inRN with general nonlinearities.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Ambrosio, Concentration phenomena for a class of fractional Kirchhoff equations inRN with general nonlinearities

Reference 3

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation fee020dd-3a25-43d5-b042-9426b4358a99 · outbound

This paper cites Chang, R.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Chang, R

Reference 4

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation cafc0065-80ea-4439-a8d2-879c382325af · outbound

This paper cites Chang, V.D.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Chang, V.D

Reference 5

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 62de7d8d-b05b-4e19-8116-af09adfc8ba5 · outbound

This paper cites Cheng, S.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Cheng, S

Reference 6

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 5e6e5403-e077-45ea-9dad-371385edcf27 · outbound

This paper cites Di Nezza, G.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Di Nezza, G

Reference 7

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 6500f04e-002d-4abf-bda4-a84cbc26f1c5 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 8

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation f11a91e5-c960-40a2-9aee-d74ef2addbe7 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 9

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 69d0e3f5-bd6a-4839-a592-63ed7d425d62 · outbound

This paper cites Fiscella, E.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Fiscella, E

Reference 10

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Observation d9719ea4-a03d-4f93-8e6c-eedacaeffd9a · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 11

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Observation e182a6f5-1b02-473b-bde4-dda02eca4898 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 12

Resolution
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Observation 106679a4-aa10-4e8f-a6aa-4cf3912af7fe · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 13

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Observation 7b80389e-57eb-4965-a610-4e955b7b7455 · outbound

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Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 14

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Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 15

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Observation 8cedc57c-edd0-402e-8559-228dc252581a · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 16

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Observation ff4568b4-93b3-4ee8-8df1-b6d932d00bde · outbound

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Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 17

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Observation 23394679-e338-40dc-a931-9423720488e6 · outbound

This paper cites Huang, Y.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Huang, Y

Reference 18

Resolution
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Source-reported events for the cited work

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Observation 8192ef56-4c44-4ab6-b5a1-23eed9bc8d0f · outbound

This paper cites Isernia, Sign-changing solutions for a fractional Kirchhoff equation.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Isernia, Sign-changing solutions for a fractional Kirchhoff equation

Reference 19

Resolution
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Observation d0e4c49e-bea0-4efe-8d43-66369f832170 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 20

Resolution
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Observation 3f1bcae8-e0be-4e04-97b3-21246f1bd13f · outbound

This paper cites Laskin, Fractional quantum mechanics and L´ evy path integrals.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Laskin, Fractional quantum mechanics and L´ evy path integrals

Reference 21

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 342ec525-5ca9-44f2-93aa-010c9b4e6509 · outbound

This paper cites Lei, Multiple positive solutions for a fractional Kirchhoff type equation with logarithmic and singular nonlinearities.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Lei, Multiple positive solutions for a fractional Kirchhoff type equation with logarithmic and singular nonlinearities

Reference 22

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 1a4ef456-1a53-4922-8fb4-9dba44808c18 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 23

Resolution
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Observation 8f29350d-a171-4ebf-aaec-c394b3e2a70b · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 24

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 2c5e09a2-f7bf-4cec-86e3-55886b82cbe1 · outbound

This paper cites L¨ u, Ground states of a Kirchhoff equation with the potential on the lattice graphs.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations L¨ u, Ground states of a Kirchhoff equation with the potential on the lattice graphs

Reference 25

Resolution
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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation cfd19060-fd08-40b3-ad02-8fb8fc883d4b · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 26

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation ef293b1d-4f42-4b93-bf0f-fb66f7e620d0 · outbound

This paper cites Ouaziz, Abdesslam and A.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Ouaziz, Abdesslam and A

Reference 27

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation bf57cd97-b705-41bd-b12b-9588609695c1 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 28

Resolution
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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 29

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 97608607-6f60-4daf-a562-a79bfbde24d3 · outbound

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Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 30

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 847eb1e6-2433-41e6-ab40-c0406d04e9e7 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 31

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 32ac1ca8-5659-43a2-a60e-2dfbf651c51b · outbound

This paper cites Shuai, Existence and multiplicity of solutions for logarithmic Schr¨ odinger equations with potential.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Shuai, Existence and multiplicity of solutions for logarithmic Schr¨ odinger equations with potential

Reference 32

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 5794648c-7d68-4784-bb2d-bc4a0dfef29f · outbound

This paper cites Wang, Solutions to discrete nonlinear Kirchhoff-Choquard equations.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Wang, Solutions to discrete nonlinear Kirchhoff-Choquard equations

Reference 33

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation f01165d8-b248-4ada-bde9-897f311f64e8 · outbound

This paper cites Wang, Solutions to discrete fractional Schr¨ odinger equations.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Wang, Solutions to discrete fractional Schr¨ odinger equations

Reference 34

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation bc689855-7424-4fdf-8c94-0e329ffb2e76 · outbound

This paper cites Wang, A class of p-Laplacian equations on lattice graphs.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Wang, A class of p-Laplacian equations on lattice graphs

Reference 35

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 1c415c6a-dbeb-410b-8419-e3ad6f0e68e1 · outbound

This paper cites Wang, Solutions to discrete nonlinear Kirchhoff-Choquard equations with power nonlinearity.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Wang, Solutions to discrete nonlinear Kirchhoff-Choquard equations with power nonlinearity

Reference 36

Resolution
verified exact
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 3cd5a2f0-03d8-4eed-8e66-98f0b4f02c3e · outbound

This paper cites Fractional logarithmic Schr\"{o}dinger equations on lattice graphs.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Fractional logarithmic Schr\"{o}dinger equations on lattice graphs

Reference 37

Resolution
verified exact
local_arxiv, observed 2026-08-05T16:23:06.729013Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation bd70fbd6-26b9-46f9-93d6-8ff99532ed55 · outbound

This paper cites Wang, Sign-changing solutions to discrete nonlinear logarithmic Kirchhoff equations.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Wang, Sign-changing solutions to discrete nonlinear logarithmic Kirchhoff equations

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T16:23:06.892897Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-05T16:23:06.563390Z digest=sha256:19248e6d9054200eb2e5f58f222fda55be4a761771a006f4934a034623a79355

Observation 35ba20f3-fb86-4051-9721-e2b93e3a2edc · outbound

This paper cites Eigenvalue estimates for the fractional Laplacian on lattice subgraphs.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Eigenvalue estimates for the fractional Laplacian on lattice subgraphs

Reference 39

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unresolved
no resolver link, observed 2026-08-05T16:23:06.568627Z

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Unavailable: canonical work link unavailable.

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Observation ca70113b-7b82-45e3-bcdd-c4354bdf5446 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 40

Resolution
unresolved
raw_fallback, observed 2026-08-05T16:23:06.877114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-05T16:23:06.573512Z digest=sha256:cd27355f97f20614771838cbe7178b92c84c039cd08381e3967bc6c396124fb7

Observation 368f19ec-f01d-4268-8448-8c617f346092 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 41

Resolution
unresolved
raw_fallback, observed 2026-08-05T16:23:06.860778Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-05T16:23:06.577890Z digest=sha256:f8b801ce86979ba29cf3c301d8d4a1edec356acd08e06ceb125ca21248c1873f

Observation d94fb814-47c6-4291-b7bc-86c0cfb1254f · outbound

This paper cites Wu, Infinitely many positive multi-bump solutions for fractional Kirchhoff equations.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Wu, Infinitely many positive multi-bump solutions for fractional Kirchhoff equations

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T16:23:06.845995Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-05T16:23:06.582954Z digest=sha256:ec1b1a6d7380114640ae290459b1d3a05f39fb92e80e627f8a1f2a715d08ec54

Observation 0895bea5-a74f-4ada-8db5-9831c6ff6943 · outbound

This paper cites Xiang, D.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Xiang, D

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T16:23:06.829816Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-05T16:23:06.587458Z digest=sha256:5f7ee83aecef0baea37cd81267a8ca33431c65200d802f50616d2d1fb2814e17

Observation a6d27eb4-a267-488b-b081-a5acec587f6f · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 44

Resolution
unresolved
raw_fallback, observed 2026-08-05T16:23:06.813919Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-05T16:23:06.591816Z digest=sha256:5453083b7058d462844d720a05f61e3cae5f1feda25b14f65b97f650048d1bb5

Observation 4438a391-89c9-4142-afed-1dd765df2833 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 45

Resolution
unresolved
raw_fallback, observed 2026-08-05T16:23:06.797984Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-05T16:23:06.596920Z digest=sha256:2f4e25535bb447eb82f58041d761a02784ca2b6bd6cf95ad0f4e307fcfa8cf13

Observation 0225fda5-f791-472a-8f88-a9f479342147 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 46

Resolution
unresolved
raw_fallback, observed 2026-08-05T16:23:06.781316Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-05T16:23:06.601806Z digest=sha256:87ec47c605abffadbe824a2072562610540b2bb12a52a85f6cc30efece73baef

Observation 00abcedb-ebb0-478c-8e97-0a7a8cb10b99 · outbound

This paper cites Zhang, X.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Zhang, X

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T16:23:06.765447Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-05T16:23:06.606501Z digest=sha256:e34366767e1a953506e585976b146f809f8c3bd7aedc295dacb7ce7c1384dca8

Observation a32a24fa-5f52-45e2-931b-8c501f6d6214 · outbound

This paper cites Fractional Laplace operator and related Schr\"odinger equations on locally finite graphs.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Fractional Laplace operator and related Schr\"odinger equations on locally finite graphs

Reference 48

Resolution
verified exact
local_arxiv, observed 2026-08-05T16:23:06.682025Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-05T16:23:06.611389Z digest=sha256:693df7ff1f192e6093423d139eff4797bd168f5ec40e5db6ba2fbf3e0bf3071a

Observation 038d6901-388a-411e-bad1-2726af87c213 · outbound

This paper cites Zloshchastiev, Logarithmic nonlinearity in theories of quantum gravity: origin of time and observational con- sequences.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Zloshchastiev, Logarithmic nonlinearity in theories of quantum gravity: origin of time and observational con- sequences

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T16:23:06.748373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-05T16:23:06.616618Z digest=sha256:068c40dd46a7d9a8fc2ac274396b6f9e1022fc5046fa36e94066962d83111eba

Pith citing papers

No inbound Pith citation observations are available.