Boundedness of solutions for nonlinear reversible system at resonance

In this paper, we are concerned with the problem of boundedness of solutions for the following nonlinear p-Laplacian: ϕp(x ) + (p − 1)npϕp(x) + f (x)ϕp(x )+ g(x) = e(t ), where ϕp(u) = |u|p−2u, p 2, for some n ∈ N, f, g ∈ C∞(R) are odd functions, e(t ) ∈ C∞(R) is odd and 2πp-periodic.  2004 Elsevier Inc. All rights reserved.