{"paper":{"title":"On the existence of sign changing bound state solutions of a quasilinear equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carmen Cort\\'azar, Cecilia Yarur, Marta Garcia-Huidobro","submitted_at":"2012-07-31T20:00:20Z","abstract_excerpt":"In this paper we establish the existence of bound state solutions of any given order to $$ \\Delta_m u +f(u)=0, x\\in R^N, N\\ge m>1, (P) $$ where $\\Delta_m u=\\nabla\\cdot(|\\nabla u|^{m-2}\\nabla u)$ using the same techniques as in [GST] to establish the existence of a ground state solution to (P). Since our solutions change sign, we assume f is continuous in R. The main point here is that by asking a stronger subcritical assumption (see (f_3)(ii) below) than the one considered in [GST], we are able to adapt their techniques to obtain the existence of bound states with a prescribed number of zeros."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0017","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"}