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− 1 p + β− 1 p = 2ω with ω = n m, m,n ∈ N, f (x,x , t) is bounded and 2πp periodic in t, where πp = 2π p sin(π/p) .  2004 Elsevier Inc. All rights reserved