{"paper":{"title":"Existence and concentration of solution for a non-local regional Schr\\\"odinger equation with competing potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"C\\'esar E. Torres Ledesma, Claudianor O. Alves","submitted_at":"2016-11-07T13:59:33Z","abstract_excerpt":"In this paper, we study the existence and concentration phenomena of solutions for the following non-local regional Schr\\\"odinger equation $$ \\left\\{ \\begin{array}{l} \\epsilon^{2\\alpha}(-\\Delta)_\\rho^{\\alpha} u + Q(x)u = K(x)|u|^{p-1}u,\\;\\;\\mbox{in}\\;\\; \\mathbb{R}^n,\\\\ u\\in H^{\\alpha}(\\mathbb{R}^n) \\end{array} \\right. $$ where $\\epsilon$ is a positive parameter, $0< \\alpha < 1$, $1<p<\\frac{n+2\\alpha}{n-2\\alpha}$, $n>2\\alpha$; $(-\\Delta)_{\\rho}^{\\alpha}$ is a variational version of the regional fractional Laplacian, whose range of scope is a ball with radius $\\rho (x)>0$, $\\rho, Q, K$ are compe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02056","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"}