Solvability of a nonlinear Volterra–Stieltjes integral equation in the class of bounded and continuous functions of two variables

Solvability of a nonlinear Volterra–Stieltjes integral equation in the class of bounded and... The aim of this paper is to investigate the solvability of a nonlinear Volterra–Stieltjes integral equation in two variables in the space $$BC(\mathbb {R_+} \times \mathbb {R_+},\mathbb {R})$$ B C ( R + × R + , R ) . We will consider this equation in the space of real continuous and bounded functions on the set $$\mathbb {R_+} \times \mathbb {R_+}$$ R + × R + . Applying the fixed point theorem of Darbo type and the technique of measure of noncompactness we will show that solutions of the mentioned equation exist. We will also give the characterization of these solutions. At the end of our considerations we will introduce some special cases of the studied equation and we will include an example illustrating our main result. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Springer Journals

Solvability of a nonlinear Volterra–Stieltjes integral equation in the class of bounded and continuous functions of two variables

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer-Verlag Italia
Subject
Mathematics; Mathematics, general; Applications of Mathematics; Theoretical, Mathematical and Computational Physics
ISSN
1578-7303
eISSN
1579-1505
D.O.I.
10.1007/s13398-017-0379-6
Publisher site
See Article on Publisher Site

Abstract

The aim of this paper is to investigate the solvability of a nonlinear Volterra–Stieltjes integral equation in two variables in the space $$BC(\mathbb {R_+} \times \mathbb {R_+},\mathbb {R})$$ B C ( R + × R + , R ) . We will consider this equation in the space of real continuous and bounded functions on the set $$\mathbb {R_+} \times \mathbb {R_+}$$ R + × R + . Applying the fixed point theorem of Darbo type and the technique of measure of noncompactness we will show that solutions of the mentioned equation exist. We will also give the characterization of these solutions. At the end of our considerations we will introduce some special cases of the studied equation and we will include an example illustrating our main result.

Journal

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. MatemáticasSpringer Journals

Published: Feb 15, 2017

References

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