Abstract
Periodic solutions of a class of integrodifferential impulsive periodic systems with time-varying generating operators on Banach space
Highlights
It is well known that impulsive periodic motion is a very important and special phenomena in natural science and in social science such as climate, food supplement, insecticide population, sustainable development
After showing the compactness of the P oincareoperator P and obtaining the boundedness of the fixed point set {x = λP x, λ ∈ [0, 1]} by virtue of the generalized Gronwall inequality, we can use Leray-Schauder fixed point theorem to establish the existence of T0-periodic P C-mild solutions for integrodifferential impulsive periodic system with time-varying generating operators
In order to study the integrodifferential impulsive periodic system with time-varying generating operators, we first recall some results about linear impulsive periodic system with time-varying generating operators here
Summary
It is well known that impulsive periodic motion is a very important and special phenomena in natural science and in social science such as climate, food supplement, insecticide population, sustainable development. We use Leray-Schauder fixed point theorem to obtain the existence of periodic solutions for integrodifferential impulsive periodic system with time-varying generating operators (1.1). By a new generalized Gronwall inequality with impulse, mixed type integral operator and B-norm given by us, the estimate of fixed point set {x = λP x, λ ∈ [0, 1]} is established. After showing the compactness of the P oincareoperator P and obtaining the boundedness of the fixed point set {x = λP x, λ ∈ [0, 1]} by virtue of the generalized Gronwall inequality, we can use Leray-Schauder fixed point theorem to establish the existence of T0-periodic P C-mild solutions for integrodifferential impulsive periodic system with time-varying generating operators. An example is given to demonstrate the applicability of our result
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