{"paper":{"title":"Existence of solution for a class of indefinite variational problems with discontinuous nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudianor O. Alves, Geovany F. Patricio","submitted_at":"2020-12-07T12:47:34Z","abstract_excerpt":"This paper concerns the existence of a nontrivial solution for the following problem\n  \\begin{equation}\n  \\left\\{\\begin{aligned}\n  -\\Delta u + V(x)u & \\in \\partial_u F(x,u)\\;\\;\\mbox{a.e. in}\\;\\;\\mathbb{R}^{N},\\nonumber\n  u \\in H^{1}(\\mathbb{R}^{N}).\n  \\end{aligned}\n  \\right.\\leqno{(P)}\n  \\end{equation} where $F(x,t)=\\int_{0}^{t}f(x,s)\\,ds$, $f$ is a $\\mathbb{Z}^{N}$-periodic Caratheodory function and $\\lambda=0$ does not belong to the spectrum of $-\\Delta+V$. Here, $\\partial_t F$ denotes the generalized gradient of $F$ with respect to variable $t$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.03641","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2012.03641/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}