Unboundedness of the large solutions of an asymmetric oscillator

In this paper, we consider the unboundedness problem of solutions for the following asymmetric oscillator: (φp(x′))′+(p−1)[αφp(x+)−βφp(x−)]=f(x,x′,t), where φp(u)=|u|p−2u, p>1, α≠β, α and β are positive constants such that α−1p+β−1p=2ω with ω=nm, m,n∈N, f(x,x′,t) is bounded and 2πp periodic in t, where πp=2πpsin(π/p).