{"paper":{"title":"Existence and asymptotic behaviour of solutions for a quasi-linear schrodinger-poisson system under a critical nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gaetano Siciliano, Giovany M. Figueiredo","submitted_at":"2017-07-17T18:30:31Z","abstract_excerpt":"In this paper we consider the following quasilinear Schr\\\"odinger-Poisson system $$ \\left\\{ \\begin{array}[c]{ll} - \\Delta u +u+\\phi u = \\lambda f(x,u)+|u|^{2^{*}-2}u &\\ \\mbox{in } \\mathbb{R}^{3} \\\\ -\\Delta \\phi -\\varepsilon^{4} \\Delta_4 \\phi = u^{2} & \\ \\mbox{in } \\mathbb{R}^{3}, \\end{array}\n  \\right. $$ depending on the two parameters $\\lambda,\\varepsilon>0$.\n  We first prove that, for $\\lambda$ larger then a certain $\\lambda^{*}>0$, there exists a solution for every $\\varepsilon>0$. Later, we study the asymptotic behaviour of these solutions whenever $\\varepsilon$ tends to zero, and we prove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05353","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"}