Combined effects in nonlinear problems arising in the study of anisotropic continuous media

We are concerned with the Lane-Emden-Fowler equation -Delta u = lambda k(x)u(q) +/- h(x)u(p) in Omega, subject to the Dirichlet boundary condition u = 0 on partial derivative Omega on. Omega, where Omega is a smooth bounded domain in R-N, k and h are variable potential functions, and 0 < q < 1 < p. Our analysis combines monotonicity methods with variational arguments. (C) 2011 Elsevier Ltd. All rights reserved.