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Existence of periodic solutions for totally nonlinear neutral differential equations with functional delay. (English) Zbl 1248.34105

Summary: We use a variant of Krasnoselskii’s fixed point theorem by T.A. Burton to show that the nonlinear neutral differential equation with functional delay \[ x'(t) = - a(t) h(x(t)) + c(t) x'(t - g(t)) + q \left( t, x(t), x(t - g(t)) \right) \] has a periodic solution.

MSC:

34K13 Periodic solutions to functional-differential equations
34K40 Neutral functional-differential equations
47N20 Applications of operator theory to differential and integral equations
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