Stability in a Special Class of Retarded Difference-Differential Equations with Interval-Valued Parameters

Global Asymptotic Stability in a Class of Difference Equations

We study the difference equation xn = [( f × g1 + g2 +h)/(g1 + f × g2 +h)](xn−1, . . . ,xn−r), n = 1,2, . . . , x1−r , . . . ,x0 > 0, where f ,g1,g2 : (R+) → R+ and h : (R+) → [0,+∞) are all continuous functions, and min1≤i≤r{ui,1/ui} ≤ f (u1, . . . ,ur) ≤ max1≤i≤r{ui,1/ui}, (u1, . . . ,ur) T ∈ (R+) . We prove that this difference equation admits c = 1 as the globally asymptotically stable equi...

Existence and impulsive stability for second order retarded differential equations

One of the most important parts of the qualitative theory in differential equations is the stability of solutions. The problem of stabilizing the solutions by imposing proper impulse controls is very important to many areas of the sciences and engineering. It is important, for instance, in pharmacokinetics, biotechnology, economics, chemical technology and others. We consider certain second ord...

On φ-stability of a class of singular difference equations

*Correspondence: [email protected] 1College of Electronic and Information Engineering, Hebei University, Baoding, 071002, China Full list of author information is available at the end of the article Abstract This paper investigates a class of singular difference equations. Using the framework of the theory of singular difference equations and cone-valued Lyapunov functions, some necessary and s...

Numerical Solutions of Special Class of Systems of Non-Linear Volterra Integro-Differential Equations by a Simple High Accuracy Method

Retarded Differential Equations with Piecewise Constant Delays

Profound and close links exist between functional and functional differential equations. Thus, the study of the first often enables one to predict properties of differential equations of neutral type. On the other hand, some methods for the latter in the special case when the deviation of the argument vanishes at individual points have been used to investigate functional equations [ 11. Functio...