{"paper":{"title":"Generalized Nehari manifold and semilinear Schr\\\"odinger equation with weak monotonicity condition on the nonlinear term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrzej Szulkin, Francisco Odair de Paiva, Wojciech Kryszewski","submitted_at":"2016-09-15T12:49:11Z","abstract_excerpt":"We study the Schr\\\"odinger equations $-\\Delta u + V(x)u = f(x,u)$ in $\\mathbb{R}^N$ and $-\\Delta u - \\lambda u = f(x,u)$ in a bounded domain $\\Omega\\subset\\mathbb{R}^N$. We assume that $f$ is superlinear but of subcritical growth and $u\\mapsto f(x,u)/|u|$ is nondecreasing. In $\\mathbb{R}^N$ we also assume that $V$ and $f$ are periodic in $x_1,\\ldots,x_N$. We show that these equations have a ground state and that there exist infinitely many solutions if $f$ is odd in $u$. Our results generalize those in \\cite{sw1} where $u\\mapsto f(x,u)/|u|$ was assumed to be strictly increasing. This seemingly"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04611","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"}