## Communications in Mathematical Analysis

### Bounded and Periodic solutions of a Class of Impulsive Periodic Population Evolution Equations of Volterra type

#### Abstract

This paper deals with a class of impulsive periodic population evolution equations of Volterra type on Banach space. By virtue of integral inequality of Gronwall type for piecewise continuous functions, the prior estimate on the $PC$-mild solutions is derived. The compactness of the new constructed Poincaré operator is shown. This allows us to apply Horn's fixed point theorem to prove the existence of $T_{0}$-periodic $PC$-mild solutions when $PC$-mild solutions are ultimate bounded. At last, an example is given for demonstration.

#### Article information

Source
Commun. Math. Anal., Volume 9, Number 1 (2010), 32-47.

Dates
First available in Project Euclid: 21 April 2010

https://projecteuclid.org/euclid.cma/1271890716

Mathematical Reviews number (MathSciNet)
MR2576913

Zentralblatt MATH identifier
1189.45016

Subjects
Primary: 45D05
Secondary: 45N05

#### Citation

Wang , JinRong; Wei, W.; Xiang, X. Bounded and Periodic solutions of a Class of Impulsive Periodic Population Evolution Equations of Volterra type. Commun. Math. Anal. 9 (2010), no. 1, 32--47. https://projecteuclid.org/euclid.cma/1271890716

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