{"paper":{"title":"Nonlinear Schr\\\"odinger equations with sum of periodic and vanishing potentials and sign-changing 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":"2016-02-16T16:20:17Z","abstract_excerpt":"We look for ground state solutions to the following nonlinear Schr\\\"{o}dinger equation $$-\\Delta u + V(x)u = f(x,u)-\\Gamma(x)|u|^{q-2}u\\hbox{ on }\\mathbb{R}^N,$$ where $V=V_{per}+V_{loc}\\in L^{\\infty}(\\mathbb{R}^N)$ is the sum of a periodic potential $V_{per}$ and a localized potential $V_{loc}$, $\\Gamma\\in L^{\\infty}(\\mathbb{R}^N)$ is periodic and $\\Gamma(x)\\geq 0$ for a.e. $x\\in\\mathbb{R}^N$ and $2\\leq q<2^*$. We assume that $\\inf\\sigma(-\\Delta+V)>0$, where $\\sigma(-\\Delta+V)$ stands for the spectrum of $-\\Delta +V$ and $f$ has the subcritical growth but higher than $\\Gamma(x)|u|^{q-2}u$, ho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05078","kind":"arxiv","version":3},"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"}