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Solvability of a Volterra-Stieltjes integral equation in the class of functions having limits at infinity. (English) Zbl 1413.74056

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.

MSC:

74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics
45G10 Other nonlinear integral equations
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