Acta Mathematica Vietnamica

, Volume 42, Issue 3, pp 533–550 | Cite as

Periodic Solutions for Non-Autonomous Neutral Functional Differential Equations with Finite Delay

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Abstract

In this work, we study the existence of periodic solutions for some non-autonomous nonlinear partial functional differential equation of neutral type. We assume that the linear part is non-densely defined and generates an evolution family under the conditions introduced by N. Tanaka. The delayed part is assumed to be ω-periodic with respect to the first argument. Using a fixed-point theorem for multivalued mapping, some sufficient conditions are given to prove the existence of periodic solutions. An example is shown to illustrate our results.

Keywords

Evolution family Fixed-point theorem Mild solution Multivalued map Neutral equation Periodic solutions Poincaré map 

Mathematics Subject Classification (2010)

34G20 35B10 37B55 47D06 

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2017

Authors and Affiliations

  1. 1.Faculty of Sciences, Department of MathematicsMoulay Ismaïl UniversityMeknèsMorocco

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