{"paper":{"title":"Multiplicity results for elliptic problems with super-critical concave and convex nonlinearties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Abbas Moameni, Najmeh Kuhestani","submitted_at":"2017-06-26T14:10:50Z","abstract_excerpt":"We shall prove a multiplicity result for semilinear elliptic problems with a super-critical nonlinearity of the form, \\begin{equation}\\label{con-c} \\left \\{ \\begin{array}{ll} -\\Delta u =|u|^{p-2} u+\\mu |u|^{q-2}u, & x \\in \\Omega\\\\ u=0, & x \\in \\partial \\Omega \\end{array} \\right. \\end{equation} where $\\Omega\\subset \\mathbb{R}^n$ is a bounded domain with $C^2$-boundary and $1<q< 2<p.$ As a consequence of our results we shall show that, for each $p>2$, there exists $\\mu^*>0$ such that for each $\\mu \\in (0, \\mu^*)$ this problem has a sequence of solutions with a negative energy. This result was al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08385","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"}