{"paper":{"title":"Regularity and multiplicity results for fractional $(p,q)$-Laplacian equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Deepak Kumar, Divya Goel, K. Sreenadh","submitted_at":"2019-02-01T15:14:47Z","abstract_excerpt":"This article deals with the study of the following nonlinear doubly nonlocal equation:\n  \\begin{equation*}\n  (-\\Delta)^{s_1}_{p}u+\\ba(-\\Delta)^{s_2}_{q}u = \\la a(x)|u|^{\\delta-2}u+ b(x)|u|^{r-2} u,\\; \\text{ in }\\; \\Om, \\; u=0 \\text{ on } \\mathbb{R}^n\\setminus \\Om,\n  \\end{equation*}\n  where $\\Om$ is a bounded domain in $\\mathbb{R}^n$ with smooth boundary, $1< \\de \\le q\\leq p<r \\leq p^{*}_{s_1}$, with $p^{*}_{s_1}=\\ds \\frac{np}{n-ps_1}$, $0<s_2 < s_1<1$, $n> p s_1$ and $\\la, \\ba>0$ are parameters. Here $a\\in L^{\\frac{r}{r-\\de}}(\\Om)$ and $b\\in L^{\\infty}(\\Om)$ are sign changing functions. We pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00395","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"}