Abstract:
In this work, the boundary value problem for a differential equation with a deviating argument, namely with an argument transformation which is an involution, is studied. Differential equations with a deviating argument occur in the modelling of various physical and geophysical processes, economic problems, and are important in the description of medical models, where the deviation of the argument is of particular importance. The question of solvability of the problem in the required class of functions, by the method of separation of variables, is reduced to the solvability of the equivalent problem for an ordinary differential equation with an involutive deviation of the argument. The theorems establishing existence and uniqueness of the solution of the problem under study are proved.
Keywords:differential equations, deviating argument, involution, boundary value problem, method of separation of variables.
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