We propose an approach for studying positivity of Green’s operators of a nonlocal boundary value problem for the system of $n$ linear functional differential equations with the boundary conditions $n_i{x}_i-{\sum }_{j=1}^n{m}_{ij}{x}_j={\beta }_i$, $i=1,\cdots ,n$, where $n_i$ and $m_{ij}$ are linear bounded “local” and “nonlocal“ functionals, respectively, from the space of absolutely continuous functions. For instance, $n_i{x}_i=x_i\left(\omega \right)$ or $n_i{x}_i=x_i\left(0\right)-x_i\left(\omega \right)$ and $m_{ij}{x}_j={\int }_0^{\omega }k\left(s\right)x_j\left(s\right)\mathrm{d}s+{\sum }_{r=1}^{n_{ij}}{c}_{ijr}{x}_j\left(t_{ijr}\right)$ can be considered. It is demonstrated that the positivity of Green’s operator of nonlocal problem follows from the positivity of Green’s operator...

We consider preservation of exponential stability for the scalar nonoscillatory linear equation with several delays $$\dot{x}\left(t\right)+\sum _{k=1}^m{a}_k\left(t\right)x\left(h_k\left(t\right)\right)=0,a_k\left(t\right)\ge 0$$ under the addition of new terms and a delay perturbation. We assume that the original equation has a positive fundamental function; our method is based on Bohl-Perron type theorems. Explicit stability conditions are obtained.

For linear differential and functional-differential equations of the $n$-th order criteria of equivalence with respect to the pointwise transformation are derived.

The aim of this paper is to give a complete proof of the formula for the resolvent of a nonautonomous linear delay functional differential equations given in the book of Hale and Verduyn Lunel [9] under the assumption alone of the continuity of the right-hand side with respect to the time,when the notion of solution is a differentiable function at each point, which satisfies the equation at each point, and when the initial value is a continuous function.

Under suitable conditions we prove the wellposedness of small time-varied delay equations and then establish the robust stability for such systems on the phase space of continuous vector-valued functions.

We establish new efficient conditions sufficient for the unique solvability of the initial value problem for two-dimensional systems of linear functional differential equations with monotone operators.

Some Wintner and Nehari type oscillation criteria are established for the second-order linear delay differential equation.

In this paper, stability of linear neutral systems with distributed delay is investigated. A bounded half circular region which includes all unstable characteristic roots, is obtained. Using the argument principle, stability criteria are derived which are necessary and sufficient conditions for asymptotic stability of the neutral systems. The stability criteria need only to evaluate the characteristic function on a straight segment on the imaginary axis and the argument on the boundary of a bounded...

The “freezing” method for ordinary differential equations is extended to multivariable retarded systems with distributed delays and slowly varying coefficients. Explicit stability conditions are derived. The main tool of the paper is a combined usage of the generalized Bohl-Perron principle and norm estimates for the fundamental solutions of the considered equations.

The “freezing” method for ordinary differential equations is extended to multivariable retarded systems with distributed delays and slowly varying coefficients. Explicit stability conditions are derived. The main tool of the paper is a combined usage of the generalized Bohl-Perron principle and norm estimates for the fundamental solutions of the considered equations.