The article describes the most interesting, in the author's opinion, results obtained by Yu.S. Kolesov, devoted to differential equations (common, functional-differential, with partial derivatives) and their applications to the mathematical ecology, radiophysics, automatic regulation, mechanics.

This paper contain the description of non-split even-homogeneous supermanifolds over the complex projective line whose retract corresponds to a holomorphic vector bundle of the signature (k,k, 2,0), where k >= 2. We prove that there are no non-split homogeneous supermanifolds in this case. See [3] and [4] for more information about the complex supermanifolds theory.

A spectral boundary problem of special type containing a spectral parameter in the boundary condition is completely solved in this paper. The characteristic equation for spectrum points determination is obtained, the energy innerproduct is derived, and the orthonormal system of the eigenfunctions is built up.

In this paper the direct theorem of the approximation theory for functions from the dyadic Besov space is proved. Together with the inverse theorem, it allows to solve an interpolation problem between dyadic BMO and the dyadic Besov space.

In this paper we present a corrected version of the theorem from the article "A Correction For Period Of Oscillation In The Model Of Spiking Neuron", in which a new first-order estimation for the oscillation period in the difference-differential model of the spiking neuron was obtained.

In this paper we calculate the oscilation period for the spiking neuron equation with constant external electric stimulus. We obtain a more precise estimation for the oscilation period.

The article is devoted to the problem of integer-valued balancing of a three-dimensional matrix. A problem of reducing this problem to the problem of finding a maximum flow in network is explored.

In this paper we prove the existence of automaton 3-counter machines which have non-semilinear reachability sets.

We consider Bernoulli measures with equally probable symbols and obtain a closed-form expression of the Grassberger entropy estimator variance.

The system of phase differences for a chain of diffuse weakly coupled oscillators on a stable integral manifold is constructed and analysed. It is shown by means of numerical methods that as the number of oscillators in the chain increases, the Lyapunov dimention growth is close to linear. The extensive computations performed for difference model of Ginsburg-Landau equation illustrate this result and determine the applicability limits for asymptotic methods.