On periodic solutions of sublinear Duffing equations

Rate of Decay of Stable Periodic Solutions of Duffing Equations

In this paper, we consider the second-order equations of Duffing type. Bounds for the derivative of the restoring force are given that ensure the existence and uniqueness of a periodic solution. Furthermore, the stability of the unique periodic solution is analyzed; the Supported in part by the science funds of Xi’an Jiaotong University Supported in part by the Xiao-Xiang Funds, Hunan Normal Un...

Periodic Solutions of Damped Duffing-type Equations with Singularity

We consider a second order equation of Duffing type. By applying Mawhin’s continuation theorem and a relationship between the periodic and the Dirichlet boundary value problems for second order ordinary differential equations, we prove that the given equation has at least one positive periodic solution when the singular forces exhibits certain some strong force condition near the origin and wit...

Periodic Wave Shock solutions of Burgers equations

In this paper we investigate the exact peroidic wave shock solutions of the Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parametr ε and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock type solution for the cauchy problem of the in...

Boundedness of solutions for semilinear duffing equations

Stability and Exact Multiplicity of Periodic Solutions of Duffing Equations with Cubic Nonlinearities

We study the stability and exact multiplicity of periodic solutions of the Duffing equation with cubic nonlinearities, x + cx + ax − x = h(t), (∗) where a and c > 0 are positive constants and h(t) is a positive T -periodic function. We obtain sharp bounds for h such that (∗) has exactly three ordered T -periodic solutions. Moreover, when h is within these bounds, one of the three solutions is n...