{"paper":{"title":"Dual Variational Methods for a nonlinear Helmholtz system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dominic Scheider, Rainer Mandel","submitted_at":"2017-10-12T14:08:21Z","abstract_excerpt":"This paper considers a pair of coupled nonlinear Helmholtz equations \\begin{align*}\n  -\\Delta u - \\mu u = a(x) \\left( |u|^\\frac{p}{2} + b(x) |v|^\\frac{p}{2} \\right)|u|^{\\frac{p}{2} - 2}u, \\end{align*} \\begin{align*}\n  -\\Delta v - \\nu v = a(x) \\left( |v|^\\frac{p}{2} + b(x) |u|^\\frac{p}{2} \\right)|v|^{\\frac{p}{2} - 2}v \\end{align*} on $\\mathbb{R}^N$ where $\\frac{2(N+1)}{N-1} < p < 2^\\ast$. The existence of nontrivial strong solutions in $W^{2, p}(\\mathbb{R}^N)$ is established using dual variational methods.\n  The focus lies on necessary and sufficient conditions on the parameters deciding whethe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04526","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"}