Title: 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 $\mathbb{R}^N$
($N\geq 2$). 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.