Unbounded Solutions of Asymmetric Oscillator

Abstract

We obtain sufficient conditions for the existence of unbounded solutions of the following nonlinear differential equation (φp(x′))+(p−1)[αφp(x+)−βφp(x−)]=(p−1)f(t,x,x′), where φp(u)=|u|p−2u, p>1, x+=max{x,0}, x−=max{−x,0}, α,β are positive constants, and f is continuous, bounded, and T-periodic in t for some T>0.