{"paper":{"title":"Soliton solutions for a class of quasilinear Schr\\\"{o}dinger equations with a parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudianor O. Alves, Yaotian Shen, Youjun Wang","submitted_at":"2013-09-18T10:23:01Z","abstract_excerpt":"Using variational methods combined with perturbation arguments, we study the existence of nontrivial classical solution for the quasilinear Schr\\\"{o}dinger equation\n  \\begin{equation*}\\label{1.1}\n  -\\Delta u+ V(x)u+ \\frac{\\kappa}{2}[\\Delta |u|^2]u=l(u),\\ x\\in\\mathbb{R}^N,\n  \\end{equation*} where $V:\\mathbb{R}^N\\rightarrow \\mathbb{R}$ and $l:\\mathbb{R} \\to \\mathbb{R}$ are continuous function, $\\kappa$ is a parameter and $N\\geq 3$. This model has been proposed in plasma physics and nonlinear optics. As a main novelty with respect to some previous results, we are able to deal with the case $\\kapp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4606","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"}