{"paper":{"title":"On a Kirchhoff type problems with potential well and indefinite potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yisheng Huang, Yuanze Wu, Zeng Liu","submitted_at":"2015-07-13T09:52:14Z","abstract_excerpt":"In this paper, we study the following Kirchhoff type problem:% $$ \\left\\{\\aligned&-\\bigg(\\alpha\\int_{\\bbr^3}|\\nabla u|^2dx+1\\bigg)\\Delta u+(\\lambda a(x)+a_0)u=|u|^{p-2}u&\\text{ in }\\bbr^3,\\\\% &u\\in\\h,\\endaligned\\right.\\eqno{(\\mathcal{P}_{\\alpha,\\lambda})}% $$ where $4<p<6$, $\\alpha$ and $\\lambda$ are two positive parameters, $a_0\\in\\bbr$ is a (possibly negative) constant and $a(x)\\geq0$ is the potential well. By the variational method, we investigate the existence of nontrivial solutions to $(\\mathcal{P}_{\\alpha,\\lambda})$. To our best knowledge, it is the first time that the nontrivial soluti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03373","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"}