{"paper":{"title":"Multiplicity and concentration of nontrivial solutions for the generalized extensible beam equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juntao Sun, Tsung-fang Wu","submitted_at":"2018-12-07T14:43:53Z","abstract_excerpt":"In this paper, we study a class of generalized extensible beam equations with a superlinear nonlinearity \\begin{equation*} \\left\\{ \\begin{array}{ll} \\Delta ^{2}u-M\\left( \\Vert \\nabla u\\Vert _{L^{2}}^{2}\\right) \\Delta u+\\lambda V(x) u=f( x,u) & \\text{ in }\\mathbb{R}^{N}, \\\\ u\\in H^{2}(\\mathbb{R}^{N}), & \\end{array}% \\right. \\end{equation*}% where $N\\geq 3$, $M(t) =at^{\\delta }+b$ with $a,\\delta >0$ and $b\\in \\mathbb{% R}$, $\\lambda >0$ is a parameter, $V\\in C(\\mathbb{R}^{N},\\mathbb{R})$ and $% f\\in C(\\mathbb{R}^{N}\\times \\mathbb{R},\\mathbb{R}).$ Unlike most other papers on this problem, we allo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03043","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"}