Existence and uniqueness of solution of the Cauchy problem for singular systems of integro-differential equations
Consider the system of singular integro-differential equations \[ y'= f(x, y)+ \int^ x_{0^ +} g(x, s, y(s))ds\tag{1} \] with the initial condition \(y(0^ +)= 0\), where \(y\), \(f\), and \(g\) are vector functions. The author establishes sufficient conditions for the existence of a unique solution of problem (1) in the indicated region. As an application, the asymptotics of solutions of a system of singular integro-differential equations are also investigated.
system of singular integro-differential equations
scientific article; zbMATH DE number 726974
scientific article