{"paper":{"title":"Multiplicity of positive solutions for a quasilinear Schr\\\"odinger equation with an almost 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, Uberlandio B. Severo","submitted_at":"2018-01-25T18:27:47Z","abstract_excerpt":"In this paper we prove an existence result of multiple positive solutions for the following quasilinear problem \\begin{equation*} \\left\\{ \\begin{array}[c]{ll} -\\Delta u - \\Delta (u^2)u = |u|^{p-2}u & \\mbox{ in } \\Omega u= 0 &\\mbox{ on } \\partial\\Omega, \\end{array} \\right. \\end{equation*} where $\\Omega$ is a smooth and bounded domain in $\\mathbb R^{N},N\\geq3$. More specifically we prove that, for $p$ near the critical exponent $22^{*}=4N/(N-2)$, the number of positive solutions is estimated below by topological invariants of the domain $\\Omega$: the Ljusternick-Schnirelmann category and the Poi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08516","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"}