{"paper":{"title":"Eigenvalue problem for a p-Laplacian equation with trapping potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huan-Song Zhou, Long-Jiang Gu, Xiaoyu Zeng","submitted_at":"2016-05-26T09:32:01Z","abstract_excerpt":"Consider the following eigenvalue problem of p-Laplacian equation \\begin{equation}\\label{P}\n  -\\Delta_{p}u+V(x)|u|^{p-2}u=\\mu|u|^{p-2}u+a| u|^{s-2}u, x\\in \\mathbb{R}^{n}, \\tag{P} \\end{equation} where $a\\geq0$, $p\\in (1,n)$ and $\\mu\\in\\mathbb{R}$. $V(x)$ is a trapping type potential, e.g., $\\inf\\limits_{x \\in \\mathbb{R}^n}V(x)< \\lim\\limits_{|x|\\rightarrow+\\infty}V(x)$. By using constrained variational methods, we proved that there is $a^*>0$, which can be given explicitly, such that problem (\\ref{P}) has a ground state $u$ with $\\|u\\|_{L^p}=1$ for some $\\mu \\in \\mathbb{R}$ and all $a\\in [0,a^*)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08206","kind":"arxiv","version":2},"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"}