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Keywords:
Fixed point theorem; contraction; compactness; neutral differential equation; integral equation; periodic solution; positive solution; stability
Fixed point theorem; contraction; compactness; neutral differential equation; integral equation; periodic solution; positive solution; stability
Summary:
Our paper deals with the following nonlinear neutral differential equation with variable delay \[ \frac{d}{dt}Du_{t}(t) =p (t)-a(t)u (t)-a(t) g(u(t-\tau (t))) -h (u(t) ,u (t-\tau (t))) . \] By using Krasnoselskii’s fixed point theorem we obtain the existence of periodic solution and by contraction mapping principle we obtain the uniqueness. A sufficient condition is established for the positivity of the above equation. Stability results of this equation are analyzed. Our results extend and complement some results obtained in the work [Yuan, Y., Guo, Z.: On the existence and stability of periodic solutions for a nonlinear neutral functional differential equation Abstract and Applied Analysis 2013, ID 175479 (2013), 1–8.].
References:
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