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

Canadian mathematical bulletin

Muhammad N. Islam¹ 

[1] Department of Mathematics, University of Dayton, Dayton, OH 45469-2316 USA

关键词: Volterra integral equation;    periodic solutions;    Liapunov's method;    Krasnosel'skii's fixed point theorem;    Schaefer's fixed point theorem;   

DOI  :  10.4153/CMB-2011-123-5

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

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.

【 授权许可】

Unknown