THE ESTIMATES OF SOLUTIONS OF A SYSTEM OF LINEAR INTEGRO-DIFFERENTIAL EQUATIONS OF THE FIRST ORDER OF TYPE VOLTERRA-STYLTIES ON THE SEMI-AXIS
Sufficient conditions are established that make it possible to estimate all solutions of a system of linear integro-differential equations of the first order of Volterra-Stieltjes type on the semiaxis. These conditions are obtained in the form of «signs of the function and absolute integration of the function on the semiaxis», which is easily verified. Also used are square matrix shapes. The article develops the methods of S. Iskandarov (1995) of matrix weight functions and cutting functions, the method of integral inequalities with the Volterra-Stieltjes integral. In this system, the integration in the equations is performed over an increasing function and the definition of A. Asanov (2001) is used. The corresponding results of Zh.O. Tolubaev's Ph.D. thesis (2016) are generalized. Estimates similar to those in this paper were provided by S. Iskandarov (1995) for a system of Voltaire-type integro-differential equations, and no one has proposed estimates for Volterra-Stieltjes-type systems using the scalar function «known as asymptotic properties». This is how the value of the grades obtained in the article is determined. We believe that it is not difficult to verify the conditions of the theorem in the article.