O některých vlastnostech lineárních diferenciálních rovnic
On exactness of upper estimates of the characteristic exponent of a linear system with exponentially decreasing perturbations.
On stable polynomials
The article is a survey on problem of the theorem of Hurwitz. The starting point of explanations is Schur's decomposition theorem for polynomials. It is showed how to obtain the well-known criteria on the distribution of roots of polynomials. The theorem on uniqueness of constants in Schur's decomposition seems to be new.
On the asymptotic properties of solutions of nonlinear systems
On the decay rate of solutions of non-autonomous differential systems.
On the number of zeros of Melnikov functions
We provide an effective uniform upper bound for the number of zeros of the first non-vanishing Melnikov function of a polynomial perturbations of a planar polynomial Hamiltonian vector field. The bound depends on degrees of the field and of the perturbation, and on the order of the Melnikov function. The generic case was considered by Binyamini, Novikov and Yakovenko [BNY10]. The bound follows from an effective construction of the Gauss-Manin connection for iterated integrals.
On the sensitivity of the matrix exponential problem
On the stability of convex symmetric polytopes of matrices.
On the stability of solutions to a class of nonlinear difference systems.
On -stability of nonlinear Lyapunov matrix differential equations.
Ordinary dichotomy and perturbations of the coefficient matrix of the linear impulsive differential equation.
Ordinary dichotomy and perturbations of the coefficient matrix of the linear impulsive differential equation
Oscillation and asymptotic properties of strongly sublinear differential equations with deviating arguments
Oб инвариантности характеристических показателей линейных систем при экспоненциально убывающих возмущениях