{"paper":{"title":"Quasilinear Schr\\\"odinger-Poisson system under an exponential critical nonlinearity: existence and asymptotic of solutions","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":"2018-02-20T19:15:02Z","abstract_excerpt":"In this paper we consider the following quasilinear Schr\\\"odinger-Poisson system in a bounded domain in $\\mathbb{R}^{2}$: $$ \\left\\{ \\begin{array}[c]{ll} - \\Delta u +\\phi u = f(u) &\\ \\mbox{in } \\Omega, -\\Delta \\phi - \\varepsilon^{4}\\Delta_4 \\phi = u^{2} & \\ \\mbox{in } \\Omega, u=\\phi=0 & \\ \\mbox{on } \\partial\\Omega \\end{array}\n  \\right. $$ depending on the parameter $\\varepsilon>0$. The nonlinearity $f$ is assumed to have critical exponencial growth. We first prove existence of nontrivial solutions $(u_{\\varepsilon}, \\phi_{\\varepsilon})$ and then we show that as $\\varepsilon\\to0^{+}$ these solu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07289","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"}