Existence of nontrivial solutions for generalized quasilinear Schrödinger equations with critical growth
type: Item
instance of: scholarly article
title: Existence of nontrivial solutions for generalized quasilinear Schrödinger equations with critical growth
zbMATH Open document ID: 1406.35363
DOI: 10.1155/2018/3615085
author: Quanqing Li
author: Xian Wu
author: Kaimin Teng
published in: Advances in Mathematical Physics
publication date: 2018-12-11T00:00:00Z
review text: Summary: We study the following generalized quasilinear Schrödinger equations with critical growth \(-\operatorname{div}(g^2 (u) \nabla u)+g(u) g' (u)|\nabla u |^2 +V (x) u = \lambda f(x,u)+g(u)| G(u)|^{2^\ast -2} G(u)\), \(x \in \mathbb R^N\), where \(\lambda >0\), \(N \geq 3\), \(g(s) : \mathbb R \rightarrow \mathbb R^+\) is a \(C^1\) even function, \(g(0)=1\), and \(g'(s)\geq 0\) for all \( \geq 0\), where \(G(u):=\int_0^u g(t) d t\). Under some suitable conditions, we prove that the equation has a nontrivial solution by variational method.
Mathematics Subject Classification ID: 35Q55
zbMATH DE Number: 6991951
zbMATH Keywords: quasilinear Schrödinger equations
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/3615085
OpenAlex ID: W2781966700
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description: scientific article; zbMATH DE number 6991951