Nonlinear elliptic equations with asymmetric asymptotic behavior at $pminfty$

Abstract

We consider a nonlinear, nonhomogeneous Dirichlet problem with reaction which is asymptotically superlinear at $+infty$ and sublinear at $-infty$. Using minimax methods together with suitable truncation techniques and Morse theory, we show that the problem has at least three nontrivial solutions one of which is negative.