Compactly Supported Solutions near a Nehari Critical Value

Abstract

We study non-negative solutions of the indefinite sublinear Dirichlet problem $$\{\begin{array}{ll}-\Delta u=\lambda u+m(x)|u{|}^{\alpha -1}u& in\; \Omega ,\\ u=0& on\partial \Omega ,\end{array}$$ where $\Omega \subset {\mathbb{R}}^N$ is a smooth bounded domain, $0<\alpha <1$, $m\in L^{\infty }(\Omega )$ is a sign-changing or non-positive weight, and $\lambda \in \mathbb{R}$.

46 Pages, 3 figures