Boundedness in nonlinear oscillations

In this paper, the boundedness of all solutions of the nonlinear differential equation (φ_p(x′))′ + αφ_p(x⁺) – βφ_p(x^–) + f(x) = e(t) is studied, where φ_p(u) = |u|^p–2 u, p ≥ 2, α, β are positive constants such that = 2w^–1 with w ∈ ?⁺?, f is a bounded C⁵ function, e(t) ∈ C⁶ is 2π_p‐periodic, x⁺ = max{x, 0}, x^– = max{–x, 0}. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)