First-order impulsive ordinary differential equations with advanced arguments

Order Ordinary Differential Equations

The DI methods for directly solving a system ofa general higher order ODEs are discussed. The convergence of the constant stepsize and constant order formulation of the DI methods is proven first before the convergencefor the variable order and stepsize case.

Second-order Differential Equations with Deviating Arguments

where f ∈ C(J ×R×R,R) and α∈ C(J , J) (e.g., αmay be defined by α(t)=√t, T ≥ 1 or α(t)= 0.7t, t ∈ J). Moreover, r and γ are fixed real numbers. Differential equations with deviated arguments arise in a variety of areas of biological, physical, and engineering applications, see, for example, [9, Chapter 2]. The monotone iterative method is useful to obtain approximate solutions of nonlinear diff...

Oscillation of nonlinear impulsive differential equations with piecewise constant arguments

denotes the greatest integer function, and x−1, x0 are given real numbers. Since 1980’s differential equations with piecewise constant arguments have attracted great deal of attention of researchers in mathematical and some of the others fields in science. Piecewise constant systems exist in a widely expanded areas such as biomedicine, chemistry, mechanical engineering, physics, etc. These kind...

On Exact Controllability of First-Order Impulsive Differential Equations

Impulsive Boundary-value Problems for First-order Integro-differential Equations

This article concerns boundary-value problems of first-order nonlinear impulsive integro-differential equations: y′(t) + a(t)y(t) = f(t, y(t), (Ty)(t), (Sy)(t)), t ∈ J0, ∆y(tk) = Ik(y(tk)), k = 1, 2, . . . , p,