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Under certain assumptions on $V$ and $f$, we obtain infinitely many high energy solutions for \\eqref{eq*} without assuming the"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1507.01205","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-05T11:46:55Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"8a15a3012a1fcce239b50093374ff751f003ce10b779961c846ff90cd69d5876","abstract_canon_sha256":"ec1687341f9dc00dd17ef0bbd9c5bc4c04e343d82770265fc8abe5aafa93e18f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:17.729926Z","signature_b64":"fBHmKWhK/uDNIlq5JgCVt5jxNt0XgGkkGuP5JasKMiZPgG64dnEZ93CZx7fNO3CyluJTny21xWa381MhihJHBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"486dd33945bc095fd754515c8fd793d9cca3632b78c77c44c7a3430a51267ab7","last_reissued_at":"2026-05-18T01:37:17.729225Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:17.729225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence and multiplicity results for the fractional Schrodinger-Poisson systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Jinguo Zhang","submitted_at":"2015-07-05T11:46:55Z","abstract_excerpt":"This paper is devoted to study the existence and multiplicity solutions for the nonlinear\n  Schr\\\"odinger-Poisson systems involving fractional Laplacian operator: \\begin{equation}\\label{eq*}\n  \\left\\{ \\aligned\n  &(-\\Delta)^{s} u+V(x)u+ \\phi u=f(x,u), \\quad &\\text{in }\\mathbb{R}^3,\n  &(-\\Delta)^{t} \\phi=u^2, \\quad &\\text{in }\\mathbb{R}^3,\n  \\endaligned\n  \\right. \\end{equation} where $(-\\Delta)^{\\alpha}$ stands for the fractional Laplacian of order $\\alpha\\in (0\\,,\\,1)$. 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