{"paper":{"title":"Existence and multiplicity of solutions for fractional Schr\\\"odinger-Kirchhoff equations with Trudinger-Moser nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.AP","authors_text":"Binlin Zhang, Du\\v{s}an Repov\\v{s}, Mingqi Xiang","submitted_at":"2019-06-19T07:02:16Z","abstract_excerpt":"We study the existence and multiplicity of solutions for a class of fractional Schr\\\"{o}dinger-Kirchhoff type equations with the Trudinger-Moser nonlinearity. More precisely, we consider \\begin{gather*} \\begin{cases} M\\big(\\|u\\|^{N/s}\\big)\\left[(-\\Delta)^s_{N/s}u+V(x)|u|^{\\frac{N}{s}-1}u\\right]= f(x,u) +\\lambda h(x)|u|^{p-2}u\\, &{\\rm in}\\ \\ \\mathbb{R}^N,\\\\ \\|u\\|=\\left(\\iint_{\\mathbb{R}^{2N}}\\frac{|u(x)-u(y)|^{N/s}}{|x-y|^{2N}}dxdy+\\int_{\\mathbb{R}^N}V(x)|u|^{N/s}dx\\right)^{s/N}, \\end{cases}\\end{gather*} where $M:[0,\\infty]\\rightarrow [0,\\infty)$ is a continuous function, $s\\in (0,1)$, $N\\geq2$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.07943","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"}