{"paper":{"title":"A Nehari manifold for non-local elliptic operator with concave-convex non-linearities and sign-changing weight function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"K.Sreenadh, Sarika Goyal","submitted_at":"2013-07-19T07:54:27Z","abstract_excerpt":"In this article, we study the existence and multiplicity of non-negative solutions of following $p$-fractional equation: $$ \\quad \\left\\{\\begin{array}{lr}\\ds\n  \\quad - 2\\int_{\\mb R^n}\\frac{|u(y)-u(x)|^{p-2}(u(y)-u(x))}{|x-y|^{n+p\\al}} dxdy = \\la h(x)|u|^{q-1}u+ b(x)|u|^{r-1} u \\; \\text{in}\\; \\Om\n  \\quad \\quad \\quad \\quad u \\geq 0 \\; \\mbox{in}\\; \\Om,\\quad u\\in W^{\\al,p}(\\mb R^n),\n  \\quad \\quad\\quad \\quad\\quad u =0\\quad\\quad \\text{on} \\quad \\mb R^n\\setminus \\Om \\end{array} \\right. $$ where $\\Om$ is a bounded domain in $\\mb R^n$, $p\\geq 2$, $n> p\\al$, $\\al\\in(0,1)$, $0< q<p-1 <r < \\frac{np}{n-ps}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5149","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"}