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

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.

Existence of positive solutions of a third order nonlinear differential equation with positive and negative terms

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.  

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