{"paper":{"title":"Infinitely many positive solutions of nonlinear Schr\\\"{o}dinger equations with non-symmetric potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Manuel del Pino, Wei Yao","submitted_at":"2013-09-27T10:26:51Z","abstract_excerpt":"We consider the standing-wave problem for a nonlinear Schr\\\"{o}dinger equation, corresponding to the semilinear elliptic problem \\begin{equation*} -\\Delta u+V(x)u=|u|^{p-1}u,\\ u\\in H^1(\\mathbb{R}^2), \\end{equation*} where $V(x)$ is a uniformly positive potential and $p>1$. Assuming that \\begin{equation*} V(x)=V_\\infty+\\frac{a}{|x|^m}+O\\Big(\\frac{1}{|x|^{m+\\sigma}}\\Big),\\ \\text{as}\\ |x|\\rightarrow+\\infty, %\\tag{$V2$} \\end{equation*} for instance if $p>2$, $m>2$ and $\\sigma>1$ we prove the existence of infinitely many positive solutions. If $V(x)$ is radially symmetric, this result was proved in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7196","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"}