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Study of periodic and nonnegative periodic solutions of nonlinear neutral functional differential equations via fixed points. (English) Zbl 1359.34073

Summary: In this paper, we study the existence of periodic and non-negative periodic solutions of the nonlinear neutral differential equation \[ {d \over dt}x(t)=- a(t)h(x(t)) + {d \over dt}Q(t,x(t-\tau(t)))+G(t,x(t),x(t-\tau(t))). \] We invert this equation to construct a sum of a completely continuous map and a large contraction which is suitable for applying the modificatition of Krasnoselskii’s theorem. The Carathéodory condition is used for the functions \(Q\) and \(G\).

MSC:

34K13 Periodic solutions to functional-differential equations
34K40 Neutral functional-differential equations
47H10 Fixed-point theorems
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