{"paper":{"title":"Existence and concentration phenomena 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":"2018-01-24T18:26:51Z","abstract_excerpt":"In this paper we are interested to prove the existence and concentration of ground state solution for the following class of problems $$ -\\Delta u+V(x)u=A(\\epsilon x)f(u), \\quad x \\in \\R^{N}, \\eqno{(P)_{\\epsilon}} $$ where $N \\geq 2$, $\\epsilon>0$, $A:\\R^{N}\\rightarrow\\R$ is a continuous function that satisfies $$ 0<\\inf_{x\\in\\R^{N}}A(x)\\leq\\lim_{|x|\\rightarrow+\\infty}A(x)<\\sup_{x\\in\\R^{N}}A(x)=A(0),\\eqno{(A)} $$ $f:\\R\\rightarrow\\R$ is a continuous function having critical growth, $V:\\R^{N}\\rightarrow\\R$ is a continuous and $\\Z^{N}$--periodic function with $0\\notin\\sigma(\\Delta+V)$. By using v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08138","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"}