{"paper":{"title":"Ground states of nonlinear Schr\\\"odinger equations with sum of periodic and inverse-square potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jaros{\\l}aw Mederski, Qianqiao Guo","submitted_at":"2014-12-18T19:30:06Z","abstract_excerpt":"We study the existence of solutions of the following nonlinear Schr\\\"odinger equation \\begin{equation*}\n  -\\Delta u + \\Big(V(x)-\\frac{\\mu}{|x|^2}\\Big) u = f(x,u)\n  \\hbox{ for } x\\in\\mathbb{R}^N\\setminus\\{0\\}, \\end{equation*} where $V:\\mathbb{R}^N\\to\\mathbb{R}$ and $f:\\mathrm{R}^N\\times\\mathbb{R}\\to\\mathbb{R}$ are periodic in $x\\in\\mathbb{R}$. We assume that $0$ does not lie in the spectrum of $-\\Delta+V$ and $\\mu<\\frac{(N-2)^2}{4}$, $N\\geq 3$. The superlinear and subcritical term $f$ satisfies a weak monotonicity condition. For sufficiently small $\\mu\\geq 0$ we find a ground state solution as "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6022","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"}