Multiple positive radial solutions on annuli for nonlinear Neumann problems with large growth

Abstract

We consider a classical semilinear elliptic equation with Neumann boundary conditions on an annulus in RN. The nonlinear term is the product of a radially symmetric coefficient with a pure power. We prove that if the power is sufficiently large, the problem admits at least three distinct positive and radial solutions. In case the coefficient is constant, we show that none of the three solutions is constant. The methods are variational and are based on the study of a suitable limit problem.