Non-autonomous perturbations for a class of quasilinear elliptic equations on R

This paper is concerned with the existence of two positive solutions for a class of quasilinear elliptic equations on R involving the p-Laplacian, with a non-autonomous perturbation. The first solution is obtained as a local minimum in a neighborhood of 0 and the second one by a mountain-pass argument. The special features of the problem here is the "complex" structure of the linear part which, in particular, oblige to work into the space W-1,W- (p) (R). Then one faces problems in the convergence of the sequences of derivatives u'(n) -> u. (C) 2008 Elsevier Inc. All rights reserved.