# 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

, Volume 112 (2) – Feb 15, 2017
19 pages

/lp/springer_journal/solvability-of-a-nonlinear-volterra-stieltjes-integral-equation-in-the-efCQWuh0UY
Publisher
Springer Milan
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

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Unlimited reading Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere. ### Stay up to date Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates. ### Organize your research It’s easy to organize your research with our built-in tools. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. ### Monthly Plan • Read unlimited articles • Personalized recommendations • No expiration • Print 20 pages per month • 20% off on PDF purchases • Organize your research • Get updates on your journals and topic searches$49/month

14-day Free Trial

Best Deal — 39% off

### Annual Plan

• All the features of the Professional Plan, but for 39% off!
• Billed annually
• No expiration
• For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588$360/year

billed annually

14-day Free Trial