Two sequences of solutions for indefinite superlinear-sublinear elliptic equations with nonlinear boundary conditions

Abstract

In this paper, we study semilinear elliptic equations with nonlinear Neumann boundary conditions. We prove the existence of a sequence of solutions converging to zero if the nonlinear term is locally sublinear and the existence of a sequence of solutions diverging to infinity if the nonlinear term is locally superlinear.