Existence of infinitely solutions for a modified nonlinear Schrodinger equation via dual approach

In this article, we focus on the existence of infinitely many weak solutions for the modified nonlinear Schrodinger equation $$ -\Delta u+V(x) u-[\Delta(1+u^2)^{\alpha/2}]\frac{\alpha u}{2(1+u^2) ^{\frac{2-\alpha}2}}=f(x,u),\quad \text{in } \mathbb{R}^N, $$ where $1\leq\alpha<2$, $f \in C(\mathbb...

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Bibliographic Details
Published inElectronic journal of differential equations Vol. 2018; no. 147; pp. 1 - 15
Main Authors Xinguang Zhang, Lishan Liu, Yonghong Wu, Yujun Cui
Format Journal Article
LanguageEnglish
Published Texas State University 31.07.2018
Subjects
critical point theorem
dual approach
Modified nonlinear Schrodinger equation
multiplicity
variational methods
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ISSN1072-6691

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Summary:In this article, we focus on the existence of infinitely many weak solutions for the modified nonlinear Schrodinger equation $$ -\Delta u+V(x) u-[\Delta(1+u^2)^{\alpha/2}]\frac{\alpha u}{2(1+u^2) ^{\frac{2-\alpha}2}}=f(x,u),\quad \text{in } \mathbb{R}^N, $$ where $1\leq\alpha<2$, $f \in C(\mathbb{R}^N \times \mathbb{R}, \mathbb{R})$. By using a symmetric mountain pass theorem and dual approach, we prove that the above equation has infinitely many high energy solutions.
ISSN:1072-6691