{"paper":{"title":"Infinitely many solutions of a class of elliptic equations with variable exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Chang-Mu Chu, Haidong Liu","submitted_at":"2018-10-19T08:35:53Z","abstract_excerpt":"This paper is concerned with the $p(x)$-Laplacian equation of the form \\begin{equation}\\label{eq0.1} \\left\\{\\begin{array}{ll} -\\Delta_{p(x)} u=Q(x)|u|^{r(x)-2}u, &\\mbox{in}\\ \\Omega,\\\\ u=0, &\\mbox{on}\\ \\partial \\Omega, \\end{array}\\right. \\end{equation} where $\\Omega\\subset\\R^N$ is a smooth bounded domain, $1<p^-=\\min_{x\\in\\overline{\\Omega}}p(x)\\leq p(x)\\leq\\max_{x\\in\\overline{\\Omega}}p(x)=p^+<N$, $1\\leq r(x)<p^{*}(x)=\\frac{Np(x)}{N-p(x)}$, $r^-=\\min_{x\\in \\overline{\\Omega}}r(x)<p^-$, $r^+=\\max_{x\\in\\overline{\\Omega}}r(x)>p^+$ and $Q: \\overline{\\Omega}\\to\\R$ is a nonnegative continuous function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08397","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"}