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Search: All articles in the CMB digital archive with keyword periodic solutions

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1. 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

2. CMB 2010 (vol 53 pp. 367)

Stamov, Gani Tr.
Almost Periodicity and Lyapunov's Functions for Impulsive Functional Differential Equations with Infinite Delays
This paper studies the existence and uniqueness of almost periodic solutions of nonlinear impulsive functional differential equations with infinite delay. The results obtained are based on the Lyapunov--Razumikhin method and on differential inequalities for piecewise continuous functions.

Keywords:almost periodic solutions, impulsive functional differential equations
Categories:34K45, 34B37

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