Solution of multi-delay systems via combined block-pulse functions and Legendre polynomials.
Solution semigroup and invariant manifolds for functional equations with infinite delay
It is proved that parabolic equations with infinite delay generate -semigroup on the space of initial conditions, such that local stable and unstable manifolds can be constructed for a fully nonlinear problems with help of usual methods of the theory of parabolic equations.
Solutions and Green's functions for boundary value problems of second-order four-point functional difference equations.
Solutions of an advance-delay differential equation and their asymptotic behaviour
The paper considers a scalar differential equation of an advance-delay type where constants , , and are positive, and and are arbitrary. The behavior of its solutions for is analyzed provided that the transcendental equation has a positive real root. An exponential-type function approximating the solution is searched for to be used in proving the existence of a semi-global solution. Moreover, the lower and upper estimates are given for such a solution.
Solutions of the neutral differential-difference equation .
Solvability and the unique solvability of a periodic type boundary value problem for first order scalar functional differential equations.
Solvability conditions of the Cauchy problem for two-dimensional systems of linear functional differential equations with monotone operators
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.
Solvability of a higher-order nonlinear neutral delay difference equation.
Solvability of a periodic type boundary value problem for first order scalar functional differential equations
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 .
Solvability of nonlinear functional boundary value problems
Some applications of the coincidence degree for set-contractions to functional differential equations of neutral type
Some basic theorems on difference-differential equations.
Some existence and uniqueness results for first-order boundary value problems for impulsive functional differential equations with infinite delay in Fréchet spaces.
Some existence results for solutions of differential inclusions with retardations
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.
Some notes on one oscillatory condition of neutral differential equations
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.
Some notes to existence and stability of the positive periodic solutions for a delayed nonlinear differential equations
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 oscillation criteria for the second-order linear delay differential equation
Some Wintner and Nehari type oscillation criteria are established for the second-order linear delay differential equation.
Some oscillation theorems for second order nonlinear differential equations with functional argument
Some Periodicity Criteria for Functional Differential Equations.