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Nonautonomous Dynamical Systems

formerly Nonautonomous and Stochastic Dynamical Systems

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Periodic Solutions for Nonlinear Evolution Equations with Non-instantaneous Impulses

Michal Fečkan
  • Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, 842 48 Bratislava, Slovakia, and Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia
  • Email:
/ JinRong Wang
  • Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, P.R. China School of Mathematics and Computer Science, Guizhou Normal College, Guiyang, Guizhou 550018, P.R. China
  • Email:
/ Yong Zhou
  • Department of Mathematics, Xiangtan University, Xiangtan, Hunan 411105, P.R. China
  • Email:
Published Online: 2014-08-15 | DOI: https://doi.org/10.2478/msds-2014-0004

Abstract

In this paper, we consider periodic solutions for a class of nonlinear evolution equations with non-instantaneous impulses on Banach spaces. By constructing a Poincaré operator, which is a composition of the maps and using the techniques of a priori estimate, we avoid assuming that periodic solution is bounded like in [1-4] and try to present new sufficient conditions on the existence of periodic mild solutions for such problems by utilizing semigroup theory and Leray-Schauder's fixed point theorem. Furthermore, existence of a global compact connected attractor for the Poincaré operator is derived.

Keywords: Nonlinear evolution equations; Non-instantaneous impulses; Periodic solutions; Attractor; Existence

References

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About the article

MSC: 34C25; 34K30; 35R12


Received: 2014-01-28

Accepted: 2014-04-30

Published Online: 2014-08-15



Citation Information: Nonautonomous Dynamical Systems, ISSN (Online) 2299-3193, DOI: https://doi.org/10.2478/msds-2014-0004. Export Citation

© 2014 Michal Fečkan et. al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

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