Periodic Solutions for Nonlinear Evolution Equations with Non-instantaneous Impulses

Michal Fečkan; JinRong Wang; Yong Zhou

Nonautonomous Dynamical Systems (2014)

  • Volume: 1, Issue: 1, page 93-101, electronic only
  • ISSN: 2353-0626

Abstract

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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.

How to cite

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Michal Fečkan, JinRong Wang, and Yong Zhou. "Periodic Solutions for Nonlinear Evolution Equations with Non-instantaneous Impulses." Nonautonomous Dynamical Systems 1.1 (2014): 93-101, electronic only. <http://eudml.org/doc/267050>.

@article{MichalFečkan2014,
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.},
author = {Michal Fečkan, JinRong Wang, Yong Zhou},
journal = {Nonautonomous Dynamical Systems},
keywords = {Nonlinear evolution equations; Non-instantaneous impulses; Periodic solutions; Attractor; Existence; nonlinear evolution equations; non-instantaneous impulses; periodic solutions; attractor; existence},
language = {eng},
number = {1},
pages = {93-101, electronic only},
title = {Periodic Solutions for Nonlinear Evolution Equations with Non-instantaneous Impulses},
url = {http://eudml.org/doc/267050},
volume = {1},
year = {2014},
}

TY - JOUR
AU - Michal Fečkan
AU - JinRong Wang
AU - Yong Zhou
TI - Periodic Solutions for Nonlinear Evolution Equations with Non-instantaneous Impulses
JO - Nonautonomous Dynamical Systems
PY - 2014
VL - 1
IS - 1
SP - 93
EP - 101, electronic only
AB - 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.
LA - eng
KW - Nonlinear evolution equations; Non-instantaneous impulses; Periodic solutions; Attractor; Existence; nonlinear evolution equations; non-instantaneous impulses; periodic solutions; attractor; existence
UR - http://eudml.org/doc/267050
ER -

References

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