Bigun Ya. I.
Ukr. Mat. Zh. - 2007. - 59, № 4. - pp. 435–446
The method of averaging over the fast variables is applied to the investigation of multifrequency systems with linearly transformed argument. We prove the existence of solutions of the initial-and boundary-value problems in a small neighborhood of the solution of the averaged problem and estimate the error of the method of averaging for slow variables.
Ukr. Mat. Zh. - 2004. - 56, № 2. - pp. 257-263
We prove the existence of a solution and obtain an estimate for the error of the averaging method for a multifrequency system with linearly transformed argument and integral boundary conditions.
Ukr. Mat. Zh. - 2000. - 52, № 3. - pp. 291-299
We establish the existence of a solution and obtain an estimate of the error of the averaging method for a multifrequency system with linearly transformed argument and multipoint boundary conditions.
Numerical-analytic method for the investigation of multipoint boundary-value problems for systems of differential equations with transformed argument
Ukr. Mat. Zh. - 1998. - 50, № 11. - pp. 1581–1584
The problem of existence and approximate construction is studied for the solution of a nonlinear system of differential equations with a transformed argument and linear multipoint boundary conditions.
Ukr. Mat. Zh. - 1998. - 50, № 2. - pp. 299–303
We justify the averaging method for systems with delay that pass through resonances in the process of evolution. We obtain an estimate of the error of the method that explicitly depends on a small parameter.
Existence, uniqueness, and dependence on a parameter of solutions of differential-functional equations with ordinary and partial derivatives
Ukr. Mat. Zh. - 1997. - 49, № 5. - pp. 715–719
For a system of quasilinear hyperbolic equations with a system of differential equations with lag, we prove theorems on the existence and uniqueness of a solution of the Cauchy problem and its continuous dependence on the initial conditions.
Ukr. Mat. Zh. - 1980. - 32, № 2. - pp. 149 - 154