Existence of periodic solutions for a second-order nonlinear neutral differential equation by the Krasnoselskii's fixed point technique
Abstract
The objective of this work is the application of Krasnoselskii's fixed point technique to prove the existence of periodic solutions of the second-order nonlinear neutral differential equation((d²)/(dt²))x(t)+p(t)(d/(dt))x(t)+q(t)x(t)=((d²)/(dt²))g(t,x(t-τ(t)))+f(t,x(t),x(t-τ(t))).
The idea of this technique is based on the inverting of the considered equation into an integral equation whose solution is recourse to Krasnoselskii's fixed point theorem. In addition, by application of the Banach principle on the inverted integral equation and under certain specified constraints we proved the uniqueness of the periodic solution.
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