Necessary and sufficient conditions for existence of exponential dichotomy of impulsive equations

Necessary and sufficient conditions for the existence of an exponential dichotomy of impulsive differential equations in a Hilbert space are found.     

Periodic solutions of quasilinear non-autonomous systems with impulses

The paper considers a system of differential equations with impulse perturbations at fixed moments in time of the form where x ? R ⁿ, ε is a small parameter, Sufficient conditions have been found for existence of the periodic solution of the given system in the critical and non-critical cases.     

Some properties of nonoscillating solutions of functional-differential equations ofn-th order

A functional-differential equation ofn-th order is considered, wheren≥2,m≥1 are integers andA _t/^t: C([t₀, ∞), R)→ R, i=1,2,...,m are functionals defined for everyt∈[t ₀, ∞). Sufficient conditions have been found for which all bounded non-oscillatory solutions and all non-oscillatory solutions of the functional-differntial equation tend to zero fort→∞.     

Stability of the general exponent of nonlinear impulsive differential equations in a Banach space

A theorem is proved which gurantees stability under small perturbations of the general exponent of impulsive nonlinear systems in a Banach space.     

A projection-iterative method for finding periodic solutions of nonlinear systems of difference-differential equations with impulses

A method is developed for finding approximately the periodic solutions of nonlinear systems of difference-differential equations with impulses at fixed moments.     

Stability of linear systems of differential equations with variable structure and impulse effect

In the present paper sufficient conditions for stability of the solutions of linear systems of differential equations with variable structure and impulse effect are found.     

Oscillation of solutions of impulsive nonlinear parabolic differential-difference equations

Sufficient conditions for oscillation of the solutions of impulsive nonlinear parabolic differential-difference equations are obtained.     

Some generalizations of integral inequalities of bellman-bihari type for functions of several variables

The paper deals with some linear as well as some non-linear generalizations of integral inequalities of Bellman-Bihari type for functions of several variables when the integration domain is a parallelepiped.     

Strong stability of impulsive systems

The strong stability of the zero solution of impulsive systems with impulses at fixed moments of time is investigated. It is proved that the existence of piecewise continuous functions with certain properties is a necessary and sufficient condition for the strong stability of the zero solution of such systems. By using differential inequalities for piecewise continuous functions, sufficient conditions for the strong stability of the zero solution are found.