Banas, Jozef; Dubiel, Agnieszka Solvability of a Volterra-Stieltjes integral equation in the class of functions having limits at infinity. (English) Zbl 1413.74056 Electron. J. Qual. Theory Differ. Equ. 2017, Paper No. 53, 17 p. (2017). Summary: The paper is devoted to the study of the solvability of a nonlinear Volterra-Stieltjes integral equation in the class of real functions defined, bounded and continuous on the real half-axis \(\mathbb{R}_+\) and having finite limits at infinity. The considered class of integral equations contains, as special cases, a few types of nonlinear integral equations. In particular, that class contains the Volterra-Hammerstein integral equation and the Volterra-Wiener-Hopf integral equation, among others. The basic tools applied in our study is the classical Schauder fixed point principle and a suitable criterion for relative compactness in the Banach space of real functions defined, bounded and continuous on \(\mathbb{R}_+\). Moreover, we utilize some facts and results from the theory of functions of bounded variation. Cited in 5 Documents MSC: 74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics 45G10 Other nonlinear integral equations Keywords:space of continuous and bounded functions; variation of function; function of bounded variation; Riemann-Stieltjes integral; criterion of relative compactness; integral equation; Schauder fixed point principle PDFBibTeX XMLCite \textit{J. Banas} and \textit{A. Dubiel}, Electron. J. Qual. Theory Differ. Equ. 2017, Paper No. 53, 17 p. (2017; Zbl 1413.74056) Full Text: DOI