{"paper":{"title":"Infinite many Blow-up solutions for a Schr\\\"odinger quasilinear elliptic problem with a non-square diffusion term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Carlos Alberto Santos, Jiazheng Zhou","submitted_at":"2016-03-03T17:33:29Z","abstract_excerpt":"In this paper, we consider existence of positive solutions for the Schr\\\"odinger quasilinear elliptic problem $$\n  \\left\\{ \\begin{array}{l} \\Delta_pu+\\Delta_p(|u|^{2\\gamma})|u|^{2\\gamma-2}u = a(x)g(u)~ \\mbox{on}~ \\mathbb{R}^N,\\\\ u>0\\ \\mbox{in}~\\mathbb{R}^N,\\ u(x)\\stackrel{\\left|x\\right|\\rightarrow \\infty}{\\longrightarrow} \\infty, \\end{array} \\right. $$ where $a(x), ~x\\in \\mathbb{R}^N$ and $g(s)~s>0$ are a nonnegative and continuous functions with $g$ being nonincreasing as well, $\\gamma>{1}/{2}$, and $N \\geq 1$. By a dual approach we establish sufficient conditions for existence and multiplici"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01193","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"}