{"paper":{"title":"Note on semiclassical states for the Schr\\\"{o}dinger equation with nonautonomous nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bartosz Bieganowski, Jaros{\\l}aw Mederski","submitted_at":"2018-08-28T07:31:28Z","abstract_excerpt":"We consider the following Schr\\\"{o}dinger equation $$ - \\hslash ^2 \\Delta u + V(x)u = \\Gamma(x) f(u) \\quad \\mathrm{in} \\ \\mathbb{R}^N, $$ where $u \\in H^1 (\\mathbb{R}^N)$, $u > 0$, $\\hslash > 0$ and $f$ is superlinear and subcritical nonlinear term. We show that if $V$ attains local minimum and $\\Gamma$ attains global maximum at the same point or $V$ attains global minimum and $\\Gamma$ attains local maximum at the same point, then there exists a positive solution for sufficiently small $\\hslash>0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09148","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"}