Existence of infinitely solutions for a modified nonlinear Schrodinger equation via dual approach
Date
2018-07-31
Authors
Zhang, Xinguang
Liu, Lishan
Wu, Yonghong
Cui, Yujun
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we focus on the existence of infinitely many weak solutions for the modified nonlinear Schrödinger equation
-∆u + V(x)u - [∆(1 + u2)α/2] αu/2(1 + u2)2-α/2 = ƒ(x, u), in ℝN,
where 1 ≤ α < 2, ƒ ∈ C(ℝN x ℝ, ℝ). By using a symmetric mountain pass theorem and dual approach, we prove that the above equation has infinitely many high energy solutions.
Description
Keywords
Modified nonlinear Schrödinger equation, Dual approach, Critical point theorems, Multiplicity, Variational methods
Citation
Zhang, X., Liu, L., Wu, Y., & Cui, Y. (2018). Existence of infinitely solutions for a modified nonlinear Schrodinger equation via dual approach. Electronic Journal of Differential Equations, 2018(147), pp. 1-15.
Rights
Attribution 4.0 International