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Three Fixed Point Theorems: Periodic Solutions of a Volterra Type Integral Equation with Infinite Heredity

  Published:2011-06-24
 Printed: Mar 2013
  • Muhammad N. Islam,
    Department of Mathematics, University of Dayton, Dayton, OH 45469-2316 USA
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Abstract

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 Volterra integral equation, periodic solutions, Liapunov's method, Krasnosel'skii's fixed point theorem, Schaefer's fixed point theorem
MSC Classifications: 45D05, 45J05 show english descriptions Volterra integral equations [See also 34A12]
Integro-ordinary differential equations [See also 34K05, 34K30, 47G20]
45D05 - Volterra integral equations [See also 34A12]
45J05 - Integro-ordinary differential equations [See also 34K05, 34K30, 47G20]
 

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