Translator Disclaimer
January/February 2015 On the boundary value problem for some quasilinear equations
Yuxia Guo, Xiangqing Liu
Adv. Differential Equations 20(1/2): 1-22 (January/February 2015).

Abstract

In this paper, we consider the boundary value problem for the following quasilinear Schrödinger equation: \begin{align*} & \int_\Omega\sum_{ij=1}^N a_{ij}(x, u)D_i uD_j\varphi dx+\frac{1}{2}\int_\Omega\sum_{ij=1}^ND_sa_{ij}(x, u)D_iuD_ju\varphi dx\\ & \notag \quad +\displaystyle\int_{\partial\Omega}g(x)u\varphi dx=\int_{\partial\Omega}f(x, u)\varphi dx, \forall \varphi\in C^\infty(\bar\Omega), \tag*{(P)} \end{align*} where $\Omega\subset\mathbb{R}^N (N\geq 3)$ is a smooth bounded domain, $D_i=\frac{\partial}{\partial x_i},$ $ D_sa_{ij}(x, s)=\frac{\partial}{\partial s}a_{ij}(x, s). $ These kind of equations include the so-called Modified Nonlinear Schrödinger Equation (MNLS). By using a perturbation method, we prove the existence of infinitely many solutions for the problem (P).

Citation

Download Citation

Yuxia Guo. Xiangqing Liu. "On the boundary value problem for some quasilinear equations." Adv. Differential Equations 20 (1/2) 1 - 22, January/February 2015.

Information

Published: January/February 2015
First available in Project Euclid: 11 December 2014

zbMATH: 1308.35104
MathSciNet: MR3297778

Subjects:
Primary: 35B45, 35J25

Rights: Copyright © 2015 Khayyam Publishing, Inc.

JOURNAL ARTICLE
22 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.20 • No. 1/2 • January/February 2015
Back to Top