Electron. J. Diff. Eqns., Vol. 2008(2008), No. 165, pp. 1-6.

Multiple solutions for quasilinear elliptic problems with nonlinear boundary conditions

Nguyen Thanh Chung

Using a recent result by Bonanno [2], we obtain a multiplicity result for the quasilinear elliptic problem
 - \Delta_p u + |u|^{p-2}u  = \lambda f(u) \quad \hbox{in } \Omega, \cr
 |\nabla u|^{p-2} \frac{\partial u}{\partial \nu}
 = \mu g(u) \quad \hbox{on } \partial\Omega,
where $\Omega$ is a bounded domain in $\mathbb R^N$, $N \geq  3$ with smooth boundary $\partial\Omega$, $\frac{\partial}{\partial\nu}$ is the outer unit normal derivative, the functions $f, g$ are $(p-1)$-sublinear at infinity ($1<p<N$), $\lambda$ and $\mu$ are positive parameters.

Submitted October 20, 2008. Published December 23, 2008.
Math Subject Classifications: 35J65, 35J20.
Key Words: Multiple solutions; quasilinear elliptic problems; nonlinear boundary conditions

Show me the PDF file (213 KB), TEX file, and other files for this article.

Nguyen Thanh Chung
Department of Mathematics and Informatics
Quang Binh University
312 Ly Thuong Kiet, Dong Hoi, Quang Binh, Vietnam
email: ntchung82@yahoo.com

Return to the EJDE web page