{"paper":{"title":"Nontrivial solutions for a class of semilinear elliptic equations with a nonlinear Goldstein-Wentzell boundary condition","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Enzo Vitillaro","submitted_at":"2026-07-30T16:33:10Z","abstract_excerpt":"The paper deals with the existence and multiplicity of nontrivial solutions for the doubly elliptic problem $$\\begin{cases} -\\Delta u=f(u) \\qquad &\\text{in $\\Omega$,}\\\\ \\phantom{-}u=0 &\\text{on $\\Gamma_0$,}\\\\ -\\Delta_\\Gamma u +\\partial_\\nu u =g(u)\\qquad &\\text{on $\\Gamma_1$,} \\end{cases} $$ where $\\Omega$ is a bounded open domain of $\\mathbb{R}^N$ ($N\\ge 2$) with $C^1$ boundary $\\Gamma=\\partial\\Omega$, with $\\Gamma=\\Gamma_0\\cup\\Gamma_1$, $\\Gamma_0\\cap\\Gamma_1=\\emptyset$, $\\Gamma_1$ being nonempty and relatively open on $\\Gamma$, $\\mathcal{H}^{N-1}(\\Gamma_0)>0$. The terms $f$ and $g$ are subcri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28709","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.28709/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}