On the existence of three nontrivial smooth solutions for nonlinear elliptic equations

Abstract

We consider a nonlinear elliptic problem with a nonsmooth potential function. The nonlinear differential operator includes as special case the p¡Laplacian. Using a variational approach based on nonsmooth critical point theory, we show the existence of at least three nontrivial smooth solutions. Two of them have constant sign (one is positive and the other is negative).