Exponential stability for a nonlinear functional differential equation

Exponential stability for a nonlinear functional differential equation

Exponential Stability in a Scalar Functional Differential Equation

We establish a criterion for the global exponential stability of the zero solution of the scalar retarded functional differential equation x (t) = L(x t) + g(t,x t) whose linear part y (t) = L(y t) generates a monotone semiflow on the phase space C = C([−r,0],R) with respect to the exponential ordering, and the nonlinearity g has at most linear growth.

Exponential Stability in a Nonlinear String Equation

We study the nonlinear wave equation utt ? c 2 uxx = (u) u(0; t) = 0 = u(; t) (0.1) with an analytic nonlinearity of the type (u) = u 3 + P k4 k u k. On each small{energy surface we consider a solution of the linearized system with initial datum having the proole of an elliptic sinus: we show that solutions starting close to the corresponding phase space trajectory remain close to it for times ...

An exponential spline for solving the fractional riccati differential equation

In this Article, proposes an approximation for the solution of the Riccati equation based on the use of exponential spline functions. Then the exponential spline equations are obtained and the differential equation of the fractional Riccati is discretized. The effect of performing this mathematical operation is obtained from an algebraic system of equations. To illustrate the benefits of the me...

Exponential stability for a class of functional differential equations