{"paper":{"title":"Standing waves for quasilinear Schr\\\"{o}inger equations with indefinite potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jian Zhou, Shibo Liu","submitted_at":"2018-01-06T06:43:09Z","abstract_excerpt":"We consider quasilinear Schr\\\"{o}dinger equations in $\\mathbb{R}^{N}$ of the form% \\[ -\\Delta u+V(x)u-u\\Delta(u^{2})=g(u)\\text{,}% \\] where $g(u)$ is $4$-superlinear. Unlike all known results in the literature, the Schr\\\"{o}dinger operator $-\\Delta+V$ is allowed to be indefinite, hence the variational functional does not satisfy the mountain pass geometry. By a local linking argument and Morse theory, we obtain a nontrivial solution for the problem. In case that $g$ is odd, we get an unbounded sequence of solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.01976","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"}