Differential inequalities for one component of solution vector for systems of linear functional differential equations.
About asymptotic and oscillation properties of the Dirichlet problem for delay partial differential equations.
Hopf bifurcation of integro-differential equations.
On the Kneser-type solutions for two-dimensional linear differential systems with deviating arguments.
On boundary value problems for -th order functional differential equations with impulses.
Maximum principles and boundary value problems for first-order neutral functional differential equations.
Positivity of Green's matrix of nonlocal boundary value problems
We propose an approach for studying positivity of Green’s operators of a nonlocal boundary value problem for the system of linear functional differential equations with the boundary conditions , , where and are linear bounded “local” and “nonlocal“ functionals, respectively, from the space of absolutely continuous functions. For instance, or and can be considered. It is demonstrated that the positivity of Green’s operator of nonlocal problem follows from the positivity of Green’s operator...
About differential inequalities for nonlocal boundary value problems with impulsive delay equations
We propose results about sign-constancy of Green's functions to impulsive nonlocal boundary value problems in a form of theorems about differential inequalities. One of the ideas of our approach is to construct Green's functions of boundary value problems for simple auxiliary differential equations with impulses. Careful analysis of these Green's functions allows us to get conclusions about the sign-constancy of Green's functions to given functional differential boundary value problems, using the...
On the dimension of the solution set to the homogeneous linear functional differential equation of the first order
Consider the homogeneous equation where is a linear bounded operator. The efficient conditions guaranteeing that the solution set to the equation considered is one-dimensional, generated by a positive monotone function, are established. The results obtained are applied to get new efficient conditions sufficient for the solvability of a class of boundary value problems for first order linear functional differential equations.
On exponential stability of second order delay differential equations
We propose a new method for studying stability of second order delay differential equations. Results we obtained are of the form: the exponential stability of ordinary differential equation implies the exponential stability of the corresponding delay differential equation if the delays are small enough. We estimate this smallness through the coefficients of this delay equation. Examples demonstrate that our tests of the exponential stability are essentially better than the known ones. This method...
Unique solvability of fractional functional differential equation on the basis of Vallée-Poussin theorem
We propose explicit tests of unique solvability of two-point and focal boundary value problems for fractional functional differential equations with Riemann-Liouville derivative.
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