Existence of periodic solutions in nonlinear asymmetric oscillations

In this paper, the existence of periodic solutions for the following nonlinear asymmetric oscillator, ( φ p ( x ′ ) ) ′ + ( p - 1 ) [ α φ p ( x + ) − β φ p ( 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 satisfying α 1 / p + β 1 / p = 2 m n , 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).