Abstract:

Let $\Omega$ be a smooth bounded domain in Rⁿ. In this article, we consider the homogeneous boundary Dirichlet problem of inhomogeneous $p$-Laplace equation $-\Delta_p u=|u|^{q-1}u+\lambda f(x)$ on $\Omega$, and identify necessary and sufficient conditions on $\Omega$ and $f(x)$ which ensure the existence, or multiplicities of nonnegative solutions for the problem under consideration.

Key words: Inhomogeneous p-Laplace equation, Dirichlet problem, nonnegative solution