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2014 | OriginalPaper | Buchkapitel

A Class of Functional-Integral Equations with Applications to a Bilocal Problem

verfasst von : Adrian Petruşel, Ioan A. Rus

Erschienen in: Topics in Mathematical Analysis and Applications

Verlag: Springer International Publishing

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Abstract

Let α ≤ a < b ≤ β be some real numbers, $K: [\alpha,\beta ] \times [\alpha,\beta ] \times [\alpha,\beta ] \times [\alpha,\beta ] \times \mathbb{R}^{m} \rightarrow \mathbb{R}^{m}$ and $g: [\alpha,\beta ] \rightarrow \mathbb{R}^{m}$ be continuous functions. In this work, using the Picard operator technique in a $\mathbb{R}_{+}^{m}$-metric space, we study the following functional-integral equation

$$\displaystyle{x(t) =\int _{ a}^{b}K(t,s,a,b,x(s))ds + g(t),\ t \in [\alpha,\beta ].}$$

As an application, the following bilocal problem

$$\displaystyle{-x''(t) + px'(t) + qx(t) = f(t,x(t)),\ t \in [\alpha,\beta ],\ \ x(a) = 0,x(b) = 0.}$$

is also discussed.

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Titel: A Class of Functional-Integral Equations with Applications to a Bilocal Problem
verfasst von: Adrian Petruşel
Ioan A. Rus
Verlag: Springer International Publishing
Buch: Topics in Mathematical Analysis and Applications
Print ISBN: 978-3-319-06553-3

Electronic ISBN: 978-3-319-06554-0

Copyright-Jahr: 2014
DOI: https://doi.org/10.1007/978-3-319-06554-0_28

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