{"paper":{"title":"Variable order nonlocal Choquard problem with variable exponents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Reshmi Biswas, Sweta Tiwari","submitted_at":"2019-07-05T14:04:03Z","abstract_excerpt":"In this article, we study the existence/multiplicity results for the following variable order nonlocal Choquard problem with variable exponents (-\\Delta)_{p(\\cdot)}^{s(\\cdot)}u(x)&=\\lambda|u(x)|^{\\alpha(x)-2}u(x)+ \\left(\\DD\\int_\\Omega\\frac{F(y,u(y))}{|x-y|^{\\mu(x,y)}}dy\\right)f(x,u(x)), x\\in \\Omega, u(x)&=0, x\\in \\mathbb R^N\\setminus\\Omega, where $\\Omega\\subset\\mathbb R^N$ is a smooth and bounded domain, $N\\geq 2$, $p,s,\\mu$ and $\\alpha$ are continuous functions on $\\mathbb R^N\\times\\mathbb R^N$ and $f(x,t)$ is Carath\\'edory function. Under suitable assumption on $s,p,\\mu,\\alpha$ and $f(x,t)$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02837","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"}