{"paper":{"title":"Existence and Concentration Solutions for a class of elliptic PDEs involving $p$-biharmonic Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Debajyoti Choudhuri, Ratan Kr Giri, Shesadev Pradhan","submitted_at":"2016-06-08T11:21:35Z","abstract_excerpt":"In this paper, we propose an existence result pertaining to a nontrivial solution to the problem \\begin{align*} \\Bigg\\{\\begin{split} & \\Delta^2_p u -\\Delta_p u + \\lambda V(x)|u|^{p-2}u = f(x,u)\\,,\\,x\\in \\mathbb{R}^N, & u \\in W^{2,p}(\\mathbb{R}^N), \\end{split} \\end{align*} where $\\lambda>0$, $p>1, N>2p$ and $V\\in C(\\mathbb{R}^N, \\mathbb{R}^+)$, $f\\in C(\\mathbb{R}^N \\times \\mathbb{R},\\mathbb{R})$ with certain properties. We also investigate the concentration of solutions to the problem on the set $V^{-1}(0)$ as $\\lambda \\rightarrow \\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02512","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"}