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Search: MSC category 45J05 ( Integro-ordinary differential equations [See also 34K05, 34K30, 47G20] )

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1. CMB Online first

Raffoul, Youssef N.
Periodic Solutions of Almost Linear Volterra Integro-dynamic Equation on Periodic Time Scales
Using Krasnoselskii's fixed point theorem, we deduce the existence of periodic solutions of nonlinear system of integro-dynamic equations on periodic time scales. These equations are studied under a set of assumptions on the functions involved in the equations. The equations will be called almost linear when these assumptions hold. The results of this papers are new for the continuous and discrete time scales.

Keywords:Volterra integro-dynamic equation, time scales, Krasnoselsii's fixed point theorem, periodic solution
Categories:45J05, 45D05

2. CMB 2011 (vol 56 pp. 80)

Islam, Muhammad N.
Three Fixed Point Theorems: Periodic Solutions of a Volterra Type Integral Equation with Infinite Heredity
In this paper we study the existence of periodic solutions of a Volterra type integral equation with infinite heredity. Banach fixed point theorem, Krasnosel'skii's fixed point theorem, and a combination of Krasnosel'skii's and Schaefer's fixed point theorems are employed in the analysis. The combination theorem of Krasnosel'skii and Schaefer requires an a priori bound on all solutions. We employ Liapunov's direct method to obtain such an a priori bound. In the process, we compare these theorems in terms of assumptions and outcomes.

Keywords:Volterra integral equation, periodic solutions, Liapunov's method, Krasnosel'skii's fixed point theorem, Schaefer's fixed point theorem
Categories:45D05, 45J05

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