On the Existence of Periodic Solutions for the Quasi-Linear Third-Order Differential Equation

ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR CERTAIN NON-LINEAR DIFFERENTIAL EQUATIONS

Here we consider some non-autonomous ordinary differential equations of order n and present some results and theorems on the existence of periodic solutions for them, which are sufficient conditions, section 1. Also we include generalizations of these results to vector differential equations and examinations of some practical examples by numerical simulation, section 2. For some special cases t...

ON TE EXISTENCE OF PERIODIC SOLUTION FOR CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS

Periodic solutions of fourth-order delay differential equation

In this paper the periodic solutions of fourth order delay differential equation of the form $ddddot{x}(t)+adddot{x}(t)+f(ddot{x}(t-tau(t)))+g(dot{x}(t-tau(t)))+h({x}(t-tau(t)))=p(t)$  is investigated. Some new positive periodic criteria are given.  

Existence of positive periodic solutions for third-order differential equation with strong singularity

where f , h are continuous function andT-periodic about t, h(t,x)≤ , g : [,T]×(,∞)→ R is an L-Carathéodory function, i.e., it is measurable in the first variable and continuous in the second variable, and for every  < r < s there exists hr,s ∈ L[,ω] such that |f (t,x(t))| ≤ hr,s for all x ∈ [r, s] and a.e. t ∈ [,ω], f is ω-periodic function about t. Equation (.) is singular at , whic...

Existence of Positive Periodic Solutions for a Third-order Delay Differential Equation

In this paper, the following third-order nonlinear delay differential equation with periodic coefficients x′′′(t) + p(t)x′′(t) + q(t)x′(t) + r(t)x(t) = f (t, x (t) , x(t− τ(t))) + c(t)x′(t− τ(t)), is considered. By employing Green’s function and Krasnoselskii’s fixed point theorem, we state and prove the existence of positive periodic solutions to the third-order delay differential equation.