# Akhmetov M. U.

### Rank criteria for the controllability of a boundary-value problem for a linear system of integro-differential equations with pulse influence

Ukr. Mat. Zh. - 2000. - 52, № 6. - pp. 723–730

We determine necessary and sufficient conditions for the solvability of boundary-value problems for a linear system of integro-differential equations with pulse influence. We prove theorems on the existence and integral representation of solutions of linear second order integral-sum Volterra equations and linear systems of integro-differential equations with pulse influence at fixed times.

### Control over linear pulse systems

Akhmetov M. U., Perestyuk N. A., Tleubergenov M. I.

Ukr. Mat. Zh. - 1995. - 47, № 3. - pp. 307–314

Rank conditions for control of linear pulse systems are established. The Pontryagin maximum principle is obtained in sufficient form. An example of control synthesis in a problem for linear pulse systems is given.

### On the smoothness of solutions of differential equations with a discontinuous right-hand side

Ukr. Mat. Zh. - 1993. - 45, № 12. - pp. 1587–1594

A method for the investigation of differential equations with a nonclassical right-hand side [1] is applied to the study of the higher-order differentiability of solutions of differential equations with discontinuous right-hand sides with respect to the initial data. We use results from the theory of differential equations with pulse influence [2].

### On a comparison method for pulse systems in the space $R^n$

Akhmetov M. U., Perestyuk N. A.

Ukr. Mat. Zh. - 1993. - 45, № 6. - pp. 753–762

A method for the study of differential equations with pulse influence on the surfaces, which was realized in [1] for a bounded domain in the phase space, is now extended to the entire space $R^n$. We prove theorems on the existence of integral surfaces in the critical case and justify the reduction principle for these equations.

### On the expansion of solutions to differential equations with discontinuous right-hand side in a series in initial data and parameters

Ukr. Mat. Zh. - 1993. - 45, № 5. - pp. 715–717

The conditions under which the solutions of equations with discontinuous right-hand sides depend on the initial data and parameters analytically are investigated. A definition is introduced, which specifies this dependence in the case where a surface of discontinuity exists.

### Periodic solutions of strongly nonlinear systems with nonclassical right-hand side in the case of a family of generating solutions

Ukr. Mat. Zh. - 1993. - 45, № 2. - pp. 202–208

The problem of the existence of periodic solutions to differential equations with pulse effects on the surfaces and to differential equations with discontinuous right-hand sides close to arbitrary nonlinear ones is studied. The existence of a family of periodic solutions to generating equations is assumed.

### Integral sets of quasilinear pulse systems

Akhmetov M. U., Perestyuk N. A.

Ukr. Mat. Zh. - 1992. - 44, № 1. - pp. 5–11

Sufficient conditions for the existence of integral sets of weakly nonlinear systems of differential equations with pulse effect on a surface are presented. The asymptotic behavior of solutions originating on integral sets and in the vicinity of these sets is investigated.

### Asymptotic representation of solutions of regularly perturbed systems of differential equations with nonclassical right-hand side

Akhmetov M. U., Perestyuk N. A.

Ukr. Mat. Zh. - 1991. - 43, № 10. - pp. 1298–1304

### Stability of periodic solutions of differential equations with impulse action on surfaces

Akhmetov M. U., Perestyuk N. A.

Ukr. Mat. Zh. - 1989. - 41, № 12. - pp. 1596–1601

### Differentiable dependence of the solutions of impulse systems on initial data

Akhmetov M. U., Perestyuk N. A.

Ukr. Mat. Zh. - 1989. - 41, № 8. - pp. 1028–1033

### Almost-periodic solutions of impulse systems

Akhmetov M. U., Perestyuk N. A.

Ukr. Mat. Zh. - 1987. - 39, № 1. - pp. 74-80

### Almost-periodic solutions of one class of systems with impulses

Akhmetov M. U., Perestyuk N. A.

Ukr. Mat. Zh. - 1984. - 36, № 4. - pp. 486 – 490