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.

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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

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