{"paper":{"title":"On the Schr\\\"odinger-Poisson system with steep potential well and indefinite potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juntao Sun, Tsung-fang Wu, Yuanze Wu","submitted_at":"2014-12-17T16:23:46Z","abstract_excerpt":"In this paper, we study the following Schr\\\"odinger-Poisson system: $$ \\left\\{\\aligned&-\\Delta u+V_\\lambda(x)u+K(x)\\phi u=f(x,u)&\\quad\\text{in }\\bbr^3,\\\\ &-\\Delta\\phi=K(x)u^2&\\quad\\text{in }\\bbr^3,\\\\ &(u,\\phi)\\in\\h\\times\\D,\\endaligned\\right.\\eqno{(\\mathcal{SP}_{\\lambda})} $$ where $V_\\lambda(x)=\\lambda a(x)+b(x)$ with a positive parameter $\\lambda$, $K(x)\\geq0$ and $f(x,t)$ is continuous including the power-type nonlinearity $|u|^{p-2}u$. By applying the method of penalized functions, the existence of one nontrivial solution for such system in the less-studied case $3<p\\leq4$ is obtained for $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5463","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"}