Ground States of Elliptic Problems Involving Non-Homogeneous Operators

We investigate the existence of ground states for functionals with a nonhomogenous principal part. Roughly speaking, we show that the Nehari manifold method requires no homogeneity on the principal part of a functional. This result is motivated by some elliptic problems involving nonhomoge-neous operators. As an application, we prove the existence of a ground state and infinitely many solutions for three classes of boundary value problems. Indiana University Mathematics Journal ©.