{"paper":{"title":"Highly oscillatory solutions of a Neumann problem for a $p$-laplacian equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alberto Boscaggin, Walter Dambrosio","submitted_at":"2014-09-19T08:07:27Z","abstract_excerpt":"We deal with a boundary value problem of the form $-\\epsilon(\\phi_p(\\epsilon u'))'+a(x)W'(u)=0,\\quad u'(0)=0=u'(1),$ where $\\phi_p(s) = \\vert s \\vert^{p-2} s$ for $s \\in \\mathbb{R}$ and $p>1$, and $W:[-1,1] \\to {\\mathbb R}$ is a double-well potential. We study the limit profile of solutions when $\\epsilon \\to 0^+$ and, conversely, we prove the existence of nodal solutions associated with any admissible limit profile when $\\epsilon$ is small enough."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5540","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"}