Periodic Solutions of Duffing Equation with an Asymmetric Nonlinearity and a Deviating Argument

Abstract EN

We study the existence of periodic solutions of the second-order differential equation x′′+ax+-bx-+g(x(t-τ))=p(t), where a,b are two constants satisfying 1/a+1/b=2/n, n∈N, τ is a constant satisfying 0≤τ<2π, g,p:R→R are continuous, and p is 2π-periodic.

When the limits limx→±∞g(x)=g(±∞) exist and are finite, we give some sufficient conditions for the existence of 2π-periodic solutions of the given equation.