Paper Citation Record · LEDGER

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator

As of 11 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 3 inbound Pith citation observations for arXiv:2501.11013.

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

pith.paper-citation-record.v1
2501.11013 v1

Coverage vector

measured 26 of 26 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T18:58:20.124891Z

measured 29 of 29 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T22:19:09.888894Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-05-21T20:54:21.633403Z

Reference resolution

26 of 26 outbound references displayed

verified exact1
verified fuzzy22
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 49a83589-fc09-4876-bff5-5c2badcee936 · outbound

This paper cites Alves, Somnath Gandal, Annunziata Loiudi ce, and Jagmo- han Tyagi.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator Alves, Somnath Gandal, Annunziata Loiudi ce, and Jagmo- han Tyagi

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T18:58:20.645806Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 119e9904-113e-4dd4-bd5a-785c3f950f9e · outbound

This paper cites A note on nonlinear critical problems involving the Grushin Subelliptic Operator: bifurcation and multiplicity results.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator A note on nonlinear critical problems involving the Grushin Subelliptic Operator: bifurcation and multiplicity results

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-08-10T18:58:20.178221Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 581f1e35-d33d-47c9-96a2-6c717e61dda4 · outbound

This paper cites A relation between pointwis e convergence of functions and convergence of functionals.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator A relation between pointwis e convergence of functions and convergence of functionals

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T18:58:20.629283Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 17b465d2-93ee-4a90-b888-7abf7ac53ac5 · outbound

This paper cites Positive solutions of no nlinear elliptic equations involving critical Sobolev exponents.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator Positive solutions of no nlinear elliptic equations involving critical Sobolev exponents

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T18:58:20.611285Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 634c18b1-ec71-44b8-b18c-f0ce6b513e59 · outbound

This paper cites Bifurcation and multiplicity results for nonlinear elliptic problems invo lving critical Sobolev exponents.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator Bifurcation and multiplicity results for nonlinear elliptic problems invo lving critical Sobolev exponents

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T18:58:20.592999Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation e01f26f7-0805-48f1-8b59-9c13a24655dc · outbound

This paper cites an unresolved cited work.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-10T18:58:20.576380Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d4669fb8-e7c1-422c-992b-e5fbf0b5e5ef · outbound

This paper cites Fadell and Paul H.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator Fadell and Paul H

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T18:58:20.558153Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 072e8417-5ea3-4d5d-85b6-893156de22a5 · outbound

This paper cites Multiplicity results for fractional Laplace problems with critical grow th.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator Multiplicity results for fractional Laplace problems with critical grow th

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T18:58:20.542624Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 84676c29-590a-4d9b-97de-90504b83c59c · outbound

This paper cites Modern methods in the calculus of variations: Lp spaces.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator Modern methods in the calculus of variations: Lp spaces

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T18:58:20.525424Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 1c07b410-c5e4-4cae-8794-f61db8401aea · outbound

This paper cites Quasilinear ellipt ic equations involving critical Sobolev exponents.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator Quasilinear ellipt ic equations involving critical Sobolev exponents

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T18:58:20.505351Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 235edb62-17d1-4728-bf87-ec90d655d24e · outbound

This paper cites P -Laplace equation for the Grushin type operator.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator P -Laplace equation for the Grushin type operator

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T18:58:20.486624Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation fadb49b2-438a-4fad-9928-0efd3975d6d8 · outbound

This paper cites Lq regularity for p-Laplace type Baouendi-Grushin equations.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator Lq regularity for p-Laplace type Baouendi-Grushin equations

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T18:58:20.468672Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 4c37db6a-adcc-4a6b-a6f1-fdae55e47549 · outbound

This paper cites Kogoj and Ermanno Lanconelli.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator Kogoj and Ermanno Lanconelli

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T18:58:20.450797Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 2a3f8085-fc0c-47db-99f7-df8d70b1cf54 · outbound

This paper cites On the equation div (|∇u|p−2∇u) + λ|u|p−2u = 0.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator On the equation div (|∇u|p−2∇u) + λ|u|p−2u = 0

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T18:58:20.431864Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 69b99722-01d4-452b-b492-048953f53adb · outbound

This paper cites Addendum: On the equation div (|∇u|p−2∇u) + λ|u|p−2u = 0 [Proc.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator Addendum: On the equation div (|∇u|p−2∇u) + λ|u|p−2u = 0 [Proc

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T18:58:20.412251Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 30a1b440-a4e2-40d8-9414-ab263ec8e7ad · outbound

This paper cites an unresolved cited work.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-10T18:58:20.393331Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation b4308553-721c-400a-936f-fd29bd0e678f · outbound

This paper cites an unresolved cited work.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-10T18:58:20.373854Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 099e4abb-1e57-42e3-af75-98388e4f7c7f · outbound

This paper cites Nontrivial critical groups in p-Laplacian problems via the Yang index.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator Nontrivial critical groups in p-Laplacian problems via the Yang index

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T18:58:20.355752Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation abc7e341-d349-4e37-ada5-24ff4b395b18 · outbound

This paper cites Agarwal, and Donal O’Regan.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator Agarwal, and Donal O’Regan

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T18:58:20.338718Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation bcef86bd-0ac1-40d3-8a18-96da38fe5231 · outbound

This paper cites Bifurc ation and mul- tiplicity results for critical fractional p-Laplacian problems.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator Bifurc ation and mul- tiplicity results for critical fractional p-Laplacian problems

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T18:58:20.318996Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 71f9404e-3d93-47ec-84ef-11c42706b692 · outbound

This paper cites Bifurc ation and multi- plicity results for critical p-Laplacian problems.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator Bifurc ation and multi- plicity results for critical p-Laplacian problems

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T18:58:20.301916Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation a9ea97b9-248c-4890-ab5e-237fedf96010 · outbound

This paper cites p-Laplacian problems where the nonlinearity crosses an eigenvalue.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator p-Laplacian problems where the nonlinearity crosses an eigenvalue

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T18:58:20.280861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 8f2f98b4-7600-4996-93d3-4538fc38c94d · outbound

This paper cites Régularité de la solution d’une équatio n non linéaire dans RN.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator Régularité de la solution d’une équatio n non linéaire dans RN

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T18:58:20.259163Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 3fe9fcc3-0314-49d5-9709-a993a33167bc · outbound

This paper cites Variational methods, volume 34 of Ergebnisse der Math- ematik und ihrer Grenzgebiete.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator Variational methods, volume 34 of Ergebnisse der Math- ematik und ihrer Grenzgebiete

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T18:58:20.239014Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 390ea844-d5bf-407a-9101-181bb9abd1c2 · outbound

This paper cites Liouville- type theorem for nonlinear elliptic equations involving p-Laplace-type Grushin operators.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator Liouville- type theorem for nonlinear elliptic equations involving p-Laplace-type Grushin operators

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T18:58:20.219206Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 2d3016e5-88f7-4044-bd47-55202f8feb6e · outbound

This paper cites Nontrivial solut ions for an asymp- totically linear ∆α-Laplace equation.

Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator Nontrivial solut ions for an asymp- totically linear ∆α-Laplace equation

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T18:58:20.199324Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Pith citing papers

Observation 2697a488-fbee-4f6e-91ad-f36b48eb9bcf · inbound

Existence and decay for a Grushin problem in $\mathbb{R}^N$ with singular, convective, critical reaction cites this paper.

Existence and decay for a Grushin problem in $\mathbb{R}^N$ with singular, convective, critical reaction Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-06T22:19:09.888894Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b651f690-efa5-4459-b979-d228fb63584f · inbound

Sharp remainder of the $L^{p}$-Poincar\'e inequality for Baouendi-Grushin vector fields cites this paper.

Sharp remainder of the $L^{p}$-Poincar\'e inequality for Baouendi-Grushin vector fields Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-06T20:55:15.154038Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f2155fa1-cf45-4704-a01f-3f1a7215230e · inbound

Bifurcation and multiplicity results for critical Grushin-Choquard problems cites this paper.

Bifurcation and multiplicity results for critical Grushin-Choquard problems Bifurcation and multiplicity results for critical problems involving the $p$-Grushin operator

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-05-21T20:54:21.634849Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.