{"paper":{"title":"Solutions for biharmonic equations with steep potential wells","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lushun Wang, Yuxia Guo, Zhongwei Tang","submitted_at":"2017-05-13T01:18:08Z","abstract_excerpt":"In this paper, we are concerned with the existence of least energy solutions for the following biharmonic equations: $$\\Delta^2 u+(\\lambda V(x)-\\delta)u=|u|^{p-2}u \\quad in\\quad \\mathbb{R}^N$$ where $N\\geq 5, 2<p\\leq\\frac{2N}{N-4}, \\lambda>0$ is a parameter, $V(x)$ is a nonnegative potential function with nonempty zero sets $\\mbox{int} V^{-1}(0)$, $0<\\delta<\\mu_0$ and $\\mu_0$ is the principle eigenvalue of $\\Delta^2$ in the zero sets $\\mbox{int} V^{-1}(0)$ of $V(x)$. Here $\\mbox{int} V^{-1}(0)$ denotes the interior part of the set $V^{-1}(0):=\\{x\\in \\mathbb{R}^N: V(x)=0\\}$. We prove that the a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04775","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"}