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Existence of periodic solutions of a scalar functional differential equation via a fixed point theorem. (English) Zbl 1145.34041
Consider the periodic scalar functional differential equation $$ \dot{y}(t)=-a(t)y(t)+f(t,y(t-\tau_1(t)),\dots, y(t-\tau_n(t))).$$ Using a fixed point theorem, the authors establishes a variety of sufficient conditions on the existence of single and multiple periodic solutions. These results improve and generalized some existing ones. Moreover, analogous results can be obtained similarly for the following periodic scalar functional differential equation, $$ \dot{y}(t)=a(t)y(t)-f(t,y(t-\tau_1(t)),\dots, y(t-\tau_n(t))). $$

34K13Periodic solutions of functional differential equations
47N20Applications of operator theory to differential and integral equations
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