Electron. J. Diff. Equ., Vol. 2014 (2014), No. 170, pp. 1-13.

Nonlinear elliptic problem of 2-q-Laplacian type with asymmetric nonlinearities

Dandan Yang, Chuanzhi Bai

Abstract:
In this article, we study the nonlinear elliptic problem of $2$- $q$-Laplacian type
$$\displaylines{ - \Delta u - \mu \Delta_q u = - \lambda |u|^{r-2} u + a u + b (u^+)^{\theta-1} \quad\hbox{in } \Omega, \cr u = 0 \quad\hbox{on } \partial \Omega, }$$
where $\Omega \subset \mathbb{R}^N$ is a bounded domain. For a is between two eigenvalues, we show the existence of three nontrivial solutions.

Submitted July 9, 2014. Published August 11, 2014.
Math Subject Classifications: 35J60, 35B38.
Key Words: Quasilinear elliptic equations with q-Laplacian; critical exponent; asymmetric nonlinearity; weak solution.

Show me the PDF file (263 KB), TEX file, and other files for this article.

Dandan Yang
School of Mathematical Science, Huaiyin Normal University
Huaian, Jiangsu 223300, China
email: ydd423@sohu.com
Chuanzhi Bai
School of Mathematical Science, Huaiyin Normal University
Huaian, Jiangsu 223300, China
email: czbai@hytc.edu.cn

Return to the EJDE web page