{"paper":{"title":"Existence results for superlinear elliptic equations with nonlinear boundary value conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Xiaohui Yu","submitted_at":"2014-10-10T08:05:29Z","abstract_excerpt":"In this paper, we study the existence of solutions for the following superlinear elliptic equation with nonlinear boundary value condition $$\n  \\left\\{ \\begin{array}{ll} -\\Delta u+u=|u|^{r-2}u &\\text{in} \\; \\Omega,\\\\ \\\\ \\frac{\\partial u}{\\partial \\nu}=|u|^{q-2}u &\\text{on}\\;\\partial\\Omega, \\end{array} \\right. $$ where $\\Omega\\subset \\mathbb R^N, N\\geq 3$ is a bounded domain with smooth boundary. We will prove the existence results for the above equation under four different cases: (i) Both $q$ and $r$ are subcritical; (ii) $r$ is critical and $q$ is subcritical; (iii) $r$ is subcritical and $q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2703","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"}