{"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 $\\alpha\\in (0\\,,\\,1)$. Under certain assumptions on $V$ and $f$, we obtain infinitely many high energy solutions for \\eqref{eq*} without assuming the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01205","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}