Existence of weak solutions for quasilinear Schrödinger equations with a parameter

Electronic Journal of Qualitative Theory of Differential Equations

卷:2020

Hongwei Yang¹  Caisheng Chen²  Hongwang Yu³  Yunfeng Wei⁴ 

[1] College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao, P.R. China;

[2] College of Science, Hohai University, Nanjing, P.R. China;

[3] College of Science, Nanjing Audit University, Nanjing, P.R. China;

[4] Nanjing Audit University, Nanjing, P.R. China;

关键词: quasilinear schrödinger equation;    variational method;    mountain-pass theorem;    $p$-laplace operator;   

DOI  :  10.14232/ejqtde.2020.1.41

来源: DOAJ

【 摘 要 】

In this paper, we study the following quasilinear Schrödinger equation of the form\begin{equation*}-\Delta_{p}u+V(x)|u|^{p-2}u-\left[\Delta_{p}(1+u^{2})^{\alpha/2}\right]\frac{\alpha u}{2(1+u^{2})^{(2-\alpha)/2}}=k(u),\qquad x\in \mathbb{R}^{N},\end{equation*}where $p$-Laplace operator $\Delta_{p}u={\rm div}(|\nabla u|^{p-2}\nabla u)\ (1

【 授权许可】

Unknown