Sign changing solutions of nonlinear elliptic equations

Abstract

This paper is concerned with a class of nonlinear elliptic Dirichlet problems approximating degenerate equations. If the degeneration set consists of $k$ connected components, by using variational methods, it is proved the existence of $k^{2}$ distinct nodal solutions, having exactly two nodal regions, whose positive and negative parts concentrate near subsets of the degeneration set.