{"paper":{"title":"Solutions of the fractional Schr\\\"odinger equation with sign-changing nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bartosz Bieganowski","submitted_at":"2016-09-29T16:31:47Z","abstract_excerpt":"We look for a solutions to a nonlinear, fractional Schr\\\"odinger equation $$(-\\Delta)^{\\alpha / 2}u + V(x)u = f(x,u)-\\Gamma(x)|u|^{q-2}u\\hbox{ on }\\mathbb{R}^N,$$ where potential $V$ is coercive or $V=V_{per} + V_{loc}$ is a sum of periodic in $x$ potential $V_{per}$ and localized potential $V_{loc}$, $\\Gamma\\in L^{\\infty}(\\mathbb{R}^N)$ is periodic in $x$, $\\Gamma(x)\\geq 0$ for a.e. $x\\in\\mathbb{R}^N$ and $2<q<2^*_\\alpha$. If $f$ has the subcritical growth, but higher than $\\Gamma(x)|u|^{q-2}u$, then we find a ground state solution being a minimizer on the Nehari manifold. Moreover we show th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09415","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"}