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Topics in Mathematical Analysis and Applications pp 609–631Cite as

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

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 94))

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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Authors and Affiliations

  1. Department of Mathematics, Babeş-Bolyai University, Kogălniceanu Street No. 1, 400084, Cluj-Napoca, Romania

    Adrian Petruşel & Ioan A. Rus

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  1. Adrian Petruşel
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  2. Ioan A. Rus
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Correspondence to Adrian Petruşel .

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Editors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  2. Department of Mathematics, University of Pécs, Pécs, Hungary

    László Tóth

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Petruşel, A., Rus, I.A. (2014). A Class of Functional-Integral Equations with Applications to a Bilocal Problem. In: Rassias, T., Tóth, L. (eds) Topics in Mathematical Analysis and Applications. Springer Optimization and Its Applications, vol 94. Springer, Cham. https://doi.org/10.1007/978-3-319-06554-0_28

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