# Bigun Ya. I.

### Existence of a solution and averaging of nonlinear multifrequency problems with delay

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.

### Averaging of Oscillation Systems with Delay and Integral Boundary Conditions

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.

### Averaging of a multifrequency boundary-value problem with linearly transformed argument

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.

### Averaging method in multifrequency systems with delay

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.

### Application of the averaging method for studying a certain class of multifrequency systems with lag

Ukr. Mat. Zh. - 1980. - 32, № 2. - pp. 149 - 154