On the Positive Periodic Solutions of the Nonlinear Duffing Equations with Delay and Variable Coefficients

Abstract

We consider the existence and nonexistence of the positive periodic solutions of the non-autonomous nonlinear Duffing equation with delay and variable coefficients $$ x''(t)-p(t)x'(t)+ q(t)x(t)=\lambda h(t)f(t,x(t-\tau(t)))+r(t), $$ It is shown that the equation has positive periodic solutions under certain conditions and no positive $T-$periodic solution under some other conditions by using a fixed theorem in cones.