## Abstract and Applied Analysis

### On a class of semilinear elliptic equations with boundary conditions and potentials which change sign

#### Abstract

We study the existence of nontrivial solutions for the problem $\Delta u=u$, in a bounded smooth domain $\Omega\subset\mathbb{R}^\mathbb{N}$, with a semilinear boundary condition given by ${\partial u}/{\partial\nu}=\lambda u-W(x)g(u)$, on the boundary of the domain, where $W$ is a potential changing sign, $g$ has a superlinear growth condition, and the parameter $\lambda\in{]}0,\lambda_1]; \lambda_1$ is the first eigenvalue of the Steklov problem. The proofs are based on the variational and min-max methods.

#### Article information

Source
Abstr. Appl. Anal., Volume 2005, Number 2 (2005), 95-104.

Dates
First available in Project Euclid: 17 May 2005

https://projecteuclid.org/euclid.aaa/1116340203

Digital Object Identifier
doi:10.1155/AAA.2005.95

Mathematical Reviews number (MathSciNet)
MR2179437

Zentralblatt MATH identifier
1128.35046

#### Citation

Ouanan, M.; Touzani, A. On a class of semilinear elliptic equations with boundary conditions and potentials which change sign. Abstr. Appl. Anal. 2005 (2005), no. 2, 95--104. doi:10.1155/AAA.2005.95. https://projecteuclid.org/euclid.aaa/1116340203