{"paper":{"title":"Semiclassical limit for the nonlinear Klein Gordon equation in bounded domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carlo R. Grisanti, Marco G. Ghimenti","submitted_at":"2010-12-27T20:59:58Z","abstract_excerpt":"We are interested to the existence of standing waves for the nonlinear Klein Gordon equation {\\epsilon}^2{\\box}{\\psi} + W'({\\psi}) = 0 in a bounded domain D. The main result of this paper is that, under suitable growth condition on W, for {\\epsilon} sufficiently small, we have at least cat(D) standing wavesfor the equation ({\\dag}), while cat(D) is the Ljusternik-Schnirelmann category."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5660","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"}