The Fredholm alternative for the $p$-Laplacian in exterior domains

Abstract

We investigate the Fredholm alternative for the $p$-Laplacian in an exterior domain which is the complement of the closed unit ball in ${\mathbb{R}}^N$ ($N\ge 2$). By employing techniques of Calculus of Variations we obtain the multiplicity of solutions. The striking difference between our case and the entire space case is also discussed.

34 pages