{"paper":{"title":"Multiplicity of negative-energy solutions for singular-superlinear Schr\\\"odinger equations with indefinite-sign potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carlos Alberto Santos, Kaye Silva, Ricardo Alves Lima","submitted_at":"2018-11-08T11:39:24Z","abstract_excerpt":"We are concerned with the multiplicity of positive solutions for the singular superlinear and subcritical Schr\\\"odinger equation\n  $$\n  \\begin{array}{c}\n  -\\Delta u +V(x)u=\\lambda a(x)u^{-\\gamma}+b(x)u^{p}~\\mbox{in}~ \\mathbb{R}^{N},\n  \\end{array}\n  $$\n  beyond the Nehari extremal value, as defined in Il'yasov [Topol. Methods Nonlinear Anal., 2017], when the potential $b \\in L^{\\infty}(\\mathbb{R}^{N})$ may change its sign, $0<a\\in L^{\\frac{2}{1+\\gamma}}(\\mathbb{R}^{N})$, $V$ is a positive continuous function, $N\\geq 3$ and $\\lambda>0$ is a real parameter. The main difficulties come from the non"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03365","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"}