Electron. J. Diff. Equ., Vol. 2013 (2013), No. 267, pp. 1-13.

Soliton solutions for a quasilinear Schrodinger equation

Duchao Liu

Abstract:
In this article, critical point theory is used to show the existence of nontrivial weak solutions to the quasilinear Schrodinger equation
$$ -\Delta_p u-\frac{p}{2^{p-1}}u\Delta_p(u^2)=f(x,u) $$
in a bounded smooth domain $\Omega\subset\mathbb{R}^{N}$ with Dirichlet boundary conditions.

Submitted June 24, 2013. Published December 5, 2013.
Math Subject Classifications: 35B38, 35D05, 35J20.
Key Words: Quasilinear Schrodinger equation; soliton solution; critical point theorem; fountain theorem; dual fountain theorem.

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Duchao Liu
School of Mathematics and Statistics
Lanzhou University, Lanzhou 730000, China
email: liuduchao@gmail.com
Phone +8613893289235, fax +8609318912481

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