A Qualitative Study of Solutions of Nonlinear Volterra Integral Equation in the Plane, from the Perspective of Shiba Bounded Variation

Abstract

In this article a nonlinear Volterra integral equation is studied in the space of functions of the bounded variation in the Shiba sense on the plane. A series of conditions is established for the functions and the kernel involved in this equation which guarantee the global existence and uniqueness of the solution in this space.