{"paper":{"title":"Multiplicity of Positive Solutions for an Obstacle Problem in R","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudianor O. Alves, Francisco Julio S.A. Corr\\^ea","submitted_at":"2013-04-18T10:51:28Z","abstract_excerpt":"In this paper we establish the existence of two positive solutions for the obstacle problem $$ \\displaystyle \\int_{\\Re}\\left[u'(v-u)'+(1+\\lambda V(x))u(v-u)\\right] \\geq \\displaystyle \\int_{\\Re} f(u)(v-u), \\forall v\\in \\Ka $$ where $f$ is a continuous function verifying some technical conditions and $\\Ka$ is the convex set given by $$ \\Ka =\\left\\{v\\in H^{1}(\\Re); v \\geq \\varphi \\right\\}, $$ with $\\varphi \\in H^{1}(\\Re)$ having nontrivial positive part with compact support in $\\Re$.\n  \\vspace{0.2cm} \\noindent \\emph{2000 Mathematics Subject Classification} : 34B18, 35A15, 46E39.\n  \\noindent \\emph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5077","kind":"arxiv","version":2},"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"}