{"paper":{"title":"Ground states of time-harmonic semilinear Maxwell equations in R^3 with vanishing permittivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jaros{\\l}aw Mederski","submitted_at":"2014-06-17T20:44:45Z","abstract_excerpt":"We investigate the existence of solutions $E:\\mathbb{R}^3\\to\\mathbb{R}^3$ of the time-harmonic semilinear Maxwell equation $$\\nabla\\times(\\nabla\\times E) + V(x) E = \\partial_E F(x,E) \\quad \\text{in}\\mathbb{R}^3,$$ where $V:\\mathbb{R}^3\\to\\mathbb{R}$, $V(x)\\leq 0$ a.e. on $\\mathbb{R}^3$, $\\nabla\\times$ denotes the curl operator in $\\mathbb{R}^3$ and $F:\\mathbb{R}^3\\times\\mathbb{R}^3\\to\\mathbb{R}$ is a nonlinear function in $E$. In particular we find a ground state solution provided that suitable growth conditions on $F$ are imposed and $L^{3/2}$-norm of $V$ is less than the best Sobolev constan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4535","kind":"arxiv","version":4},"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"}