{"paper":{"title":"On the eigenvalue problem involving the weighted $p$-Laplacian in radially symmetric domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Abhishek Sarkar, Ky Ho, Pavel Dr\\'abek","submitted_at":"2018-05-09T13:30:42Z","abstract_excerpt":"We investigate the following eigenvalue problem \\begin{align*} \\begin{cases} -\\operatorname{div}\\left( L(x) |\\nabla u| ^{p-2}\\nabla u\\right)=\\lambda K(x)|u|^{p-2}u \\quad \\text{in } A_{R_1}^{R_2} , u=0\\quad \\text{on } \\partial A_{R_1}^{R_2} , \\end{cases} \\end{align*} where $A_{R_1}^{R_2}:=\\{x\\in\\mathbb{R}^N: R_1<|x|<R_2\\}$ $(0< R_1<R_2\\leq\\infty)$, $\\lambda>0$ is a parameter, the weights $L$ and $K$ are measurable with $L$ positive a.e. in $A_{R_1}^{R_2}$ and $K$ possibly sign-changing in $A_{R_1}^{R_2}$. We prove the existence of the first eigenpair and discuss the regularity and positiveness "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03512","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"}