Advances in Differential Equations

On the boundary value problem for some quasilinear equations

Yuxia Guo and Xiangqing Liu

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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).

Article information

Source
Adv. Differential Equations Volume 20, Number 1/2 (2015), 1-22.

Dates
First available in Project Euclid: 11 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.ade/1418310441

Mathematical Reviews number (MathSciNet)
MR3297778

Zentralblatt MATH identifier
1308.35104

Subjects
Primary: 35B45: A priori estimates 35J25: Boundary value problems for second-order elliptic equations

Citation

Guo, Yuxia; Liu, Xiangqing. On the boundary value problem for some quasilinear equations. Adv. Differential Equations 20 (2015), no. 1/2, 1--22. https://projecteuclid.org/euclid.ade/1418310441.


Export citation