Periodic solutions of semilinear Duffing equations with impulsive effects

Boundedness of solutions for semilinear duffing equations

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...

Existence of Solutions of Periodic Boundary Value Problems for Impulsive Functional Duffing Equations at Nonresonance Case

This paper deals with the existence of solutions of the periodic boundary value problem of the impulsive Duffing equations: x′′ t αx′ t βx t f t, x t , x α1 t , . . . , x αn t , a.e. t ∈ 0, T , Δx tk Ik x tk , x′ tk , k 1, . . . , m, Δx′ tk Jk x tk , x′ tk , k 1, . . . , m, x i 0 x i T , i 0, 1. Sufficient conditions are established for the existence of at least one solution of above-mentioned ...

Impulsive differential equations: Periodic solutions and applications

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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...