A Nehari Approach for Asymptotically Linear Elliptic Problems

Abstract

In this paper we prove the existence of a signed ground state solution in the mountain pass level for a class of asymptotically linear elliptic problems, even when the nonlinearity is just continuous in the second variable. The (strongly) resonant and non-resonant cases are discussed under weaker conditions on the nonlinearity. A multiplicity result is also proved when f is odd with respect to the second variable.