{"paper":{"title":"Multiplicity results and sign changing solutions of non-local equations with concave-convex nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Debangana Mukherjee, Mousomi Bhakta","submitted_at":"2016-03-17T16:08:17Z","abstract_excerpt":"In this paper we prove the existence of infinitely many nontrivial solutions of the following equations driven by a nonlocal integro-differential operator $L_K$ with concave-convex nonlinearities and homogeneous Dirichlet boundary conditions \\begin{eqnarray*}\n  \\mathcal{L}_{K} u + \\mu\\, |u|^{q-1}u + \\lambda\\,|u|^{p-1}u &=& 0 \\quad\\text{in}\\quad \\Omega, \\\\[2mm]\n  u&=&0 \\quad\\mbox{in}\\quad\\mathbb{R}^N\\setminus\\Omega,\n  \\end{eqnarray*} where $\\Omega$ is a smooth bounded domain in $\\mathbb{R}^N$, $N>2s$, $s\\in(0, 1)$, $0<q<1<p\\leq \\frac{N+2s}{N-2s}$. Moreover, when $L_K$ reduces to the fractional "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05554","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"}