{"paper":{"title":"Existence and multiplicity results for fractional $p$-Kirchhoff equation with sign changing nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"K. Sreenadh, Pawan Kumar Mishra","submitted_at":"2015-02-23T05:20:24Z","abstract_excerpt":"In this paper, we show the existence and multiplicity of nontrivial, non-negative solutions of the fractional $p$-Kirchhoff problem  \\begin{equation*} \\begin{array}{rllll} M\\left(\\displaystyle\\int_{\\mathbb{R}^{2n}}\\frac{|u(x)-u(y)|^p}{\\left|x-y\\right|^{n+ps}}dx\\,dy\\right)(-\\Delta)^{s}_p u &=\\lambda f(x)|u|^{q-2}u+ g(x)\\left|u\\right|^{r-2}u\\, \\text{in} \\Omega,\\\\ u&=0 \\;\\mbox{in} \\mathbb{R}^{n}\\setminus \\Omega, \\end{array} \\end{equation*} where $(-\\Delta)^{s}_p$ is the fractional $p$-Laplace operator, $\\Omega$ is a bounded domain in $\\mathbb{R}^n$ with smooth boundary, $f \\in L^{\\frac{r}{r-q}}(\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06316","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"}