Some quasilinear elliptic equations involving multiple p-Laplacians

This paper is devoted to the study, with variational technique, of the following quasilinear elliptic problem: {-Delta(p)u - beta Delta(q)u = g(u) in R-N, u(x) -> 0 as |x| -> + infinity, where N >= 3, 1 < p < q, and p < N. We are interested in the existence of positive solutions for general nonlinearities. Specifically, we obtain the existence result for the zero mass case, which includes a large class of pure power nonlinearities. More general quasilinear problems of Born-Infeld type are also considered.