An application of the Picard operator technique to functional integral equations

Abstract

In this paper we consider a functional integral equation of the form
\[
x(t)=g(t,x(t),x(h(t)))+\int_{a}^{t} f(s,x(h(s)))ds+\int_{a}^{b} K(s,x(h(s)))ds, \ \ t \in [a,b].
\]

Using the weakly Picard operator technique we establish existence, data dependence and comparison results for the solutions of the above equation.

Authors

V.A. Ilea
(Babes Bolyai Univ.)

D. Otrocol
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy,
Technical University of Cluj-Napoca)

Keywords

Functional-integral equation; weakly Picard operators; data dependence

Cite this paper as:

V.A. Ilea, D. Otrocol, An application of the Picard operator technique to functional integral equations, J. Nonlinear Convex Anal., Vol. 18 (2017) no. 3, pp. 405-413

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About this paper

Journal

Journal of Nonlinear and Convex Analysis

Publisher Name

Yokohama, Japan

DOI
Print ISSN

1345-4773

Online ISSN

1880-5221

MR

MR3649198

ZBL

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References

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