Sentence examples for a solution of the delay from inspiring English sources

Let be a solution of the delay integral inequality (3.1).

If A ≥ 0 and ρ ( A ) < 1, then ( E − A ) − 1 ≥ 0. Theorem 3.1 Let y ∈ C [ R, R + n ] be a solution of the delay integral inequality (3) (4).

Malinowski [23] studied the existence and uniqueness result of a solution to the delay set-valued differential equation under condition that the right-hand side of the equation is Lipschitzian in the functional variable.

Let and be a solution of the following singular delay differential inequality with the initial conditions : (3.3).

Denote and let and be a solution of the following infinite delay difference inequality with the initial condition : (3.1).

Moreover, if we choose a constant vector v such that A v ≤ 1 2 A b + b θ, then u ̲ = A v can be considered as a lower solution of the delay differential equation (3.13).

The first approach is reducing a solution of a delay difference equation to the values of a solution of a delay differential equation with piecewise constant arguments at integer points.

If (x t)) is an eventually positive solution of the delay differential equation x'(t)+sum_{i=1}^{n}p_{i}(t)x t- tau_{i})=0, (2.4) then, for the same i, liminf_{trightarrowinfty}frac{x t-tau_{i})}{x(t)}< infty.

Finally, we prove the solution of the delay equation to converge to the solution of the original second order abstract differential equation as the delay parameter τ goes to zero.

This paper presents an analysis to obtain an analytical solution of the nonlinear delay differential equations and determine the effect of delay control on the vibration amplitude.

Numerical algorithms for computing the integrals involving generalized functions and for solution of the delay-integro-differential equation are developed.