Semilinear elliptic equations with dependence on the gradient

Abstract

In this article we consider elliptic equations whose nonlinear term depends on the gradient of the unknown. We assume that the nonlinearity has a asymptotically linear growth at zero and at infinity with respect to the second variable. By applying Morse theory and an iterative method, we prove the existence of nontrivial solutions.

Keywords

• Semilinear equation
• Morse theory
• critical group
• iterative method