Multiple Positive Solutions for Classes of Elliptic Systems

Jaffar Ali Shahul Hammed
Mississippi State University

Abstract: We study the existence of multiple positive solutions to systems of the form

\begin{displaymath}\begin{cases}\qquad-\Delta u =\lambda f(v), &\text{ in }\Omeg...
...\ \qquad\quad~~ u=0=v, &\text{ on}\partial \Omega . \end{cases}\end{displaymath}    

Here $ \Delta$ is the Laplacian operator, $ \lambda$ is a positive parameter, $ \Omega$ is a bounded domain in $ \mathbb{R}^n$ with smooth boundary and $ f,g$ belongs to a class of positive functions that have a combined sublinear effect at $ \infty$. Our results also easily extend to the corresponding p-Laplacian systems. We prove our results by the method of sub and super solutions.

Summer School 2006 2006-05-09