African Diaspora Journal of Mathematics

Periodic Solutions of Nondensely Nonautonomous Differential Equations with Delay

T Akrid, L. Maniar, and A. Ouhinou

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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.

Article information

Source
Afr. Diaspora J. Math. (N.S.), Volume 15, Number 1 (2013), 25-42.

Dates
First available in Project Euclid: 9 August 2013

Permanent link to this document
https://projecteuclid.org/euclid.adjm/1376053758

Mathematical Reviews number (MathSciNet)
MR3091708

Zentralblatt MATH identifier
1277.35029

Subjects
Primary: 35B10: Periodic solutions 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 34G20: Nonlinear equations [See also 47Hxx, 47Jxx]

Keywords
Evolution family stability conditions variation of constants formula Massera problem Poincaré map fixed point Theorem

Citation

Akrid, T; Maniar, L.; Ouhinou, A. Periodic Solutions of Nondensely Nonautonomous Differential Equations with Delay. Afr. Diaspora J. Math. (N.S.) 15 (2013), no. 1, 25--42. https://projecteuclid.org/euclid.adjm/1376053758


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