Existence of Periodic Solutions for the Duffing Equation with Impulses

Existence of Periodic Solutions for the Duffing Equation with Impulses

Existence and uniqueness of periodic solutions for a kind of Duffing equation with two deviating arguments

We use the coincidence degree to establish new results on the existence and uniqueness of T -periodic solutions for a kind of Duffing equation with two deviating arguments of the form x ′′ + Cx(t) + g1(t, x(t− τ1(t))) + g2(t, x(t− τ2(t))) = p(t).

Existence , uniqueness , and stability of periodic solutions of an equation of Duffing type

Abstract. We consider a second-order equation of Duffing type. Bounds for the derivative of the restoring force are given which ensure the existence and uniqueness of a periodic solution. Furthermore, the unique periodic solution is asymptotically stable with sharp rate of exponential decay. In particular, for a restoring term independent of the variable t, a necessary and sufficient condition ...

Existence and multiplicity of periodic solutions generated by impulses

and Applied Analysis 3 Remark 1.3. It is easy to see that V ′ 1 , V ′ 2 are weaker than V1 , V2 . Therefore, Theorem 1.2 improves Theorem A. Indeed, taking V t, u −|u| − |u|, 1 < γ < ς ≤ 2, Gk u −|u|, 1.3 all conditions in Theorem 1.4 are satisfied, but conditions in Theorem A cannot be satisfied. Theorem 1.4. Assume that V1 , V2 hold. Moreover, the following conditions are satisfied: V3 Vu t, ...

Existence of positive periodic solutions for a periodic logistic equation

In this paper, we study a more generalized class of periodic logistic equations. By using the method of coincidence degree, a set of sufficient conditions is obtained for the existence of positive periodic solutions of the equations which are under the consideration. 2002 Elsevier Science Inc. All rights reserved.