Solvability and the unique solvability of a periodic type boundary value problem for first order scalar functional differential equations.
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.
Nonimprovable sufficient conditions for the solvability and unique solvability of the problem are established, where is a continuous operator satisfying the Carathèodory conditions, is a continuous functional, and .
Using the topological transversality method of Granas we prove an existence result for a system of differential inclusions with retardations of the form y'' ∈ F(t,y,y',Φ(y)). The result is applied to the study of the existence of solutions to an equation of the trajectory of an r-stage rocket with retardations.
The aim of this paper is to present sufficient conditions for all bounded solutions of the second order neutral differential equations of the form (r(t)(x(t) - px(t-τ))')' - q(t)f(x(σ(t))) = 0 to be oscillatory and to compare some existing results.
The paper deals with the existence of positive ω-periodic solutions for a class of nonlinear delay differential equations. For example, such equations represent the model for the survival of red blood cells in an animal. The sufficient conditions for the exponential stability of positive ω-periodic solution are also considered.
Some Wintner and Nehari type oscillation criteria are established for the second-order linear delay differential equation.
We study oscillatory properties of solutions of the system of differential equations of neutral type.