The existence of a nontrivial solution to the p&q-Laplacian problem with nonlinearity asymptotic to up-1 at infinity in RN

We consider the following elliptic problem: [GRAPHICS] where m, n > 0, N >= 3 and 1 < q < p < N, f (x,u)/u(p-1) tends to a positive constant l as u -> +infinity. We prove in this paper that the problem possesses a ontrivial solution even if thuepnonlinearity f (x, t) does not satisfy the Ambrosetti-Rabinowitz condition: 0 <= F (x, u) equivalent to integral(u)(0) f(x, s)ds <= 1/ p + theta f (x, u)u, for (x, u) is an element of R-N x R+. (c) 2007 Elsevier Ltd. All rights reserved.