MULTIPERIODIC SOLUTIONS OF LINEAR SYSTEMS INTEGRO-DIFFERENTIAL EQUATIONS WITH c D -OPERATOR AND  -PERIOD OF HEREDITARY - Zh.А. Sartabanov; G.M.Aitenova (Academic Scientific Journal of Computer Science, 2019)
The article explores the questions of the initial problem and the problem of the multiperiodicity solutions of linear systems integro-differential equations with an operator of the form describe hereditary phenomena. Along with the equation of zeros of the operator c D are considered linear systems of homogeneous and inhomogeneous integro-differential equations, sufficient conditions are established for the unique solvability of the initial problems for them, both necessary and sufficient conditions of multiperiodic existence are obtained of the solutions. The integral representations of multiperiodic solutions of linear inhomogeneous systems are determined 1) in the particular case when the corresponding homogeneous systems have exponential dichotomy and 2) in the general case when the homogeneous systems do not have multiperiodic solutions, except for the trivial one.