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

Original Paper


The aim of this paper is to investigate the solvability of a nonlinear Volterra–Stieltjes integral equation in two variables in the space \(BC(\mathbb {R_+} \times \mathbb {R_+},\mathbb {R})\). We will consider this equation in the space of real continuous and bounded functions on the set \(\mathbb {R_+} \times \mathbb {R_+}\). 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.


Nonlinear Volterra–Stieltjes integral equation in two variables Fixed point theorem Measure of noncompactness Uniform local attractivity Asymptotic stability 

Mathematics Subject Classification

Primary 45G10 Secondary 47H08 


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Copyright information

© Springer-Verlag Italia 2017

Authors and Affiliations

  1. 1.Department of Nonlinear AnalysisRzeszów University of TechnologyRzeszówPoland

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