Existence of periodic solutions in nonlinear asymmetric oscillations

In this paper, the existence of periodic solutions for the following nonlinear asymmetric oscillator, (φp(x′))′+(p-1)[αφp(x+)−βφp(x−)+f(x)+g(x′)-h(t)]=0, is discussed, where φp(u) = |u|p−2u, p > 1 is a constant, α, β are positive constants satisfyingα1/p+β1/p=2mn,for some m, n ∈ N, f(x), g(y) are bounded local Lipschitz functions, h(t) is a continuous, and 2πp-periodic function, x± = max{±x, 0}, πp = 2π/p sin(π/p).