## Abstract and Applied Analysis

### Existence of Nontrivial Solutions and High Energy Solutions for a Class of Quasilinear Schrödinger Equations via the Dual-Perturbation Method

#### Abstract

We study the quasilinear Schrödinger equation of the form $-\Delta u+V\left(x\right)u-\Delta \left({u}^{2}\right)u=h\left(x,u\right)$, $x\in {R}^{N}$. Under appropriate assumptions on $V\left(x\right)$ and $h\left(x,u\right)$, existence results of nontrivial solutions and high energy solutions are obtained by the dual-perturbation method.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 256324, 13 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393512098

Digital Object Identifier
doi:10.1155/2013/256324

Mathematical Reviews number (MathSciNet)
MR3121525

Zentralblatt MATH identifier
1294.35020

#### Citation

Chen, Yu; Wu, Xian. Existence of Nontrivial Solutions and High Energy Solutions for a Class of Quasilinear Schrödinger Equations via the Dual-Perturbation Method. Abstr. Appl. Anal. 2013 (2013), Article ID 256324, 13 pages. doi:10.1155/2013/256324. https://projecteuclid.org/euclid.aaa/1393512098

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