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 W1,p(R). Then one faces problems in the convergence of the sequences of derivatives u n →u. © 2008 Elsevier Inc. All rights reserved.