Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia8564Research ArticleAbout Some Kind of Differential-Operator Equations with Variable CoefficientsMishinS NDepartment of Geometry and Mathematics Teaching Methodssergeymishin@rambler.ruOryol State University15012015131408092016Copyright © 2015,2015In this work a general method, allowing to find solutions of differential-operator equations of some type with variable coefficients by means of analitical vector-valued functions, is described. Examined equations include as particular case differential equations in partial derivatives, difference-differential and integral equations, and other functional-operator equations. Solutions are realized by uniformly converged functional vector-valued series, generated by set of solutions of ordinary differential equation of n-th order and some set of elements of locally convex space. Sufficient conditions of continuous dependence of solutions from generating set are found. Solution of Cauchy problem for examined equations is found as well and conditions of its uniqueness are specified. Besides that the so-called general solution of examined equations (the function of the most general view, from which any particular solution can be obtained) is found. The investigation is realized by means of characteristics (order and type) of operator and operator characteristics (operator type and operator order) of vector relative to operator. In this work in investigation a convergence of operator series relative to equicontinuous bornology is used.locally convex spaceorder and type of operatorsdifferential-operator equationequicontinuous bornologyconvergence by bornologyvector-valued functionлокально выпуклое пространствопорядок и тип операторадифференциально-операторное уравнениеравностепенно непрерывная борнологияборнологическая сходимостьвекторнозначная функция