A note of the periodic orbits of a kind of Duffing equations

Agraïments: The second author was supported by FCT Grant BPD/36072/2007. Research of AR supported in part by Centro de Matemática da Universidade do Porto (CMUP) financed by FCT through the programmes POCTI and POSI, with Portuguese and European Community structural funds.We study the periodic orbits of the modified Duffing differential equation ¨y + ay − εy3 = εh(y, y˙), with a > 0, ε a small parameter and h a C2 function in its variables

Antiperiodic Solutions for a Kind of Nonlinear Duffing Equations with a Deviating Argument and Time-Varying Delay

This paper deals with a kind of nonlinear Duffing equation with a deviating argument and time-varying delay. By using differential inequality techniques, some very verifiable criteria on the existence and exponential stability of antiperiodic solutions for the equation are obtained. Our results are new and complementary to previously known results. An example is given to illustrate the feasibility and effectiveness of our main results