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Qualitative analysis of some systems of differential equations of Volterra type

The present paper deals with some n-dimensional nonlinear autonomous and nonautonomous systems of differential equations of Volterra type. The behaviour of solutions in the corresponding neighbourhoods of an arbitrary or respective curve, on unbounded interval of independent variable, is considered. The existence and approximation of a solution, or a p-parameter (p∈ {;1, ..., n};) classes of solutions are established. The errors of the approximations are defined by the functions which can be sufficiently small ; for example, by the function alpha exp(-beta t), alpha, beta >0, t≥ a>0. The obtained results also contain an answer to the question on stability (or instability) of solutions whose existence is established, more precisely, the stability (or instability) of solutions with the function of stability (or instability) including autostability and stability along the coordinates of certain classes of solutions. The general results are presented and subsequently certain examples are considered. The theory of qualitative analysis of differential equations, including comparative equations and inequalities, and topological retraction method are used.

Differential equations of Volterra type; qualitative analysis of solutions

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