Multiple solutions for asymptotically linear elliptic equations with sign-changing weight

Abstract

We consider a semilinear Dirichlet problem driven by the Laplacian and with an indefinite (that is, sign-changing) weight and a nonlinearity which is asymptotically linear near $\pm \infty$. Using variational methods together with truncation techniques and Morse theory, we show that the problem has at least three nontrivial solutions, two of which have constant sign (one positive and the other negative).