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Boundedness, periodicity, and conditional stability of noninstantaneous impulsive evolution equations
Author(s) -
Yang Peng,
Wang JinRong,
Fečkan Michal
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6332
Subject(s) - mathematics , uniqueness , banach space , bounded function , mathematical analysis , stability (learning theory) , convergence (economics) , pure mathematics , machine learning , economics , economic growth , computer science
In this paper, we mainly study the existence, uniqueness, and conditional stability of bounded and periodic solutions for a class of noninstantaneous impulsive linear and semilinear equations with evolution family and exponential dichotomy. We utilize the weak*convergence analysis in the conjugate space and the Banach‐Alaoglu theorem to derive the existence result, and then we use the principle of compressed image to prove the uniqueness. In addition, we study the conditional stability of periodic solution with the help of the Grownwall‐Coppel inequality. Finally, we present an example of a noninstantaneous impulsive partial differential equation, which is transferred into an abstract impulsive evolution equation.