Existence of Periodic Solutions for a Second Order Nonlinear Neutral Functional Differential Equation
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چکیده
We study the existence of periodic solutions of the second order nonlinear neutral differential equation with variable delay x′′ (t) + p (t)x′ (t) + q (t)h (x (t)) = c (t)x′ (t− τ (t)) + f (t, x (t− τ (t))) . We invert the given equation to obtain an integral, but equivalent, equation from which we define a fixed point mapping written as a sum of a large contraction and a compact map. We show that such maps fit very nicely into the framework of Krasnoselskii-Burton’s fixed point theorem so that the existence of periodic solutions is conclued.
منابع مشابه
Periodic solutions for a higher order nonlinear neutral functional differential equation
In this paper, a higher order nonlinear neutral functional differential equation with distributed delay is studied by using the continuation theorem of coincidence degree theory. Some new results on the existence of periodic solutions are obtained. Keywords—Neutral functional differential equation, higher order, periodic solution, coincidence degree theory
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تاریخ انتشار 2013