Abstract
In this paper we study the Massera problem for the existence of a periodic mild solution of a class of nondensely nonautonomous semilinear differential equations with delay. We assume that the linear part satisfies the conditions introduced by Tanaka. First, we prove that the existence of a periodic solution for nonautonomous inhomogeneous linear differential equations with delay is equivalent to the existence of a bounded solution on the right half real line. Next, we undertake the analysis of the existence of periodic solutions in the semilinear case. To this end, we use a fixed point Theorem concerning setvalued maps. To illustrate the obtained results, we consider a periodic reaction diffusion equation with delay.
Citation
T Akrid. L. Maniar. A. Ouhinou. "Periodic Solutions of Nondensely Nonautonomous Differential Equations with Delay." Afr. Diaspora J. Math. (N.S.) 15 (1) 25 - 42, 2013.
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