{"paper":{"title":"Schrodinger-Kirchhoff-Poisson type systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cyril J. Batkam, Joao R. Santos Junior","submitted_at":"2015-03-25T05:08:02Z","abstract_excerpt":"In this article we study the existence of solutions to the system \\begin{equation*}\\left\\{  \\begin{array}{ll} -\\left(a+b\\int_{\\Omega}|\\nabla u|^{2}\\right)\\Delta u +\\phi u= f(x, u) &\\text{in }\\Omega \\hbox{} -\\Delta \\phi= u^{2} &\\text{in }\\Omega \\hbox{} u=\\phi=0&\\text{on }\\partial\\Omega, \\hbox{} \\end{array} \\right. \\end{equation*} where $\\Omega$ is a bounded smooth domain of $\\mathbb{R}^N$ ($N=1,2$ or $3$), $a>0$, $b\\geq0$, and $f:\\overline{\\Omega}\\times \\mathbb{R}\\to\\mathbb{R}$ is a continuous function which is $3$-superlinear. By using some variants of the mountain pass theorem established in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07280","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"}