MULTIPERIODIC SOLUTIONS OF LINEAR SYSTEMS INTEGRO-DIFFERENTIAL EQUATIONS WITH c D -OPERATOR AND -PERIOD OF HEREDITARY
Ключевые слова:integro-differential equation, hereditary, fluctuation, multiperiodic solution.
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.