This paper discusses the problem of positive periodic solutions for a class of nonlinear second order ordinary differential equations.By utilizing a fixed point theorem on cone,some existence and multiplicity results of positive periodic solutions are derived.Our results improve theorems in the literature.

Positive Periodic Solutions of Nonlinear Second Order Ordinary Differential Equations

Monotone iterative technique for second order delayed periodic problem in Banach spaces

In this paper, we are concerned with the existence of periodic solutions, stability of zero solution, asymptotic stability of zero solution, square integrability of the first derivative of solutions, and boundedness of solutions of nonlinear functional differential equations of second order by the second method of Lyapunov. We obtain sufficient conditions guaranteeing the existence of periodic solutions, stability of zero solution, asymptotic stability of zero solution, square integrability of the first derivative of solutions, and boundedness of solutions of the equations considered. We give an example for illustrations by MATLAB-Simulink, which shows the behaviors of the orbits. The findings of this paper extend and improve some results that can be found in the literature.

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New Qualitative Results for Solutions of Functional Differential Equations of Second Order

Sign-changing first derivative of positive solutions of forced second-order nonlinear differential equations

This paper deals with the existence of positive ω-periodic solutions for third-order ordinary differential equation with delay $$u'''(t)+Mu(t)=f\bigl(t,u(t),u(t-\tau) \bigr),\quad t\in {\mathbb{R}}, $$
 where $\omega>0$
 and $M>0$
 are constants, $f: {\mathbb{R}}^{3}\rightarrow {\mathbb{R}}$
 is continuous, $f(t,x,y)$
 is ω-periodic in t, and $\tau>0$
 is a constant denoting the time delay. We show the existence of positive ω-periodic solutions when $0< M<(\frac{2\pi}{\sqrt {3}\omega})^{3}$
 and f satisfies some order conditions. The discussion is based on the theory of fixed point index.

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Positive periodic solutions for third-order ordinary differential equations with delay

The existence results of positive ω-periodic solutions are obtained for the second-order functional differential equation with multiple delays , where is a positive ω-periodic function, is a continuous function which is ω-periodic in t, and are ω-periodic functions. The existence conditions concern the first eigenvalue of the associated linear periodic boundary problem. Our discussion is based on the fixed-point index theory in cones.

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Yongxiang Li

Papers

On the Existence of Positive Periodic Solutions for Second-Order Functional Differential Equations with Multiple Delays