{"paper":{"title":"Ground state solution for a class of indefinite variational problems with critical growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudianor O. Alves, Geilson F. Germano","submitted_at":"2017-04-05T12:39:45Z","abstract_excerpt":"In this paper we study the existence of ground state solution for an indefinite variational problem of the type $$ \\left\\{\\begin{array}{l} -\\Delta u+(V(x)-W(x))u=f(x,u) \\quad \\mbox{in} \\quad \\R^{N}, u\\in H^{1}(\\R^{N}), \\end{array}\\right. \\eqno{(P)} $$ where $N \\geq 2$, $V,W:\\mathbb{R}^N \\to \\mathbb{R}$ and $f:\\mathbb{R}^N \\times \\mathbb{R} \\to \\mathbb{R}$ are continuous functions verifying some technical conditions and $f$ possesses a critical growth. Here, we will consider the case where the problem is asymptotically periodic, that is, $V$ is $\\mathbb{Z}^N$-periodic, $W$ goes to 0 at infinity"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01385","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"}