On p-superlinear equations with a nonhomogeneous differential operator

Abstract

We consider a nonlinear elliptic equation driven by a nonhomogeneous differential operator and with a (p-1)-superlinear Carathéodory reaction. Our formulation incorporates as a special case equations monitored by the p-Laplacian. Using variational methods coupled with truncation techniques and comparison principles, we show that the problem has at least five nontrivial smooth solutions. © 2012 Springer Basel AG.