Nam Jip Koo

Asymptotic equivalence between two difference systems

Abstract In this paper, we study the asymptotic equivalence between the linear system Δx ( n ) = A ( n ) x ( n ) and its perturbation Δy ( n ) = A ( n ) y ( n )+ g ( n , y ( n )) by using the comparison principle and supplementary projections. Furthermore, we establish some asymptotic properties for the nonlinear system Δx ( n ) = f ( n , x ( n )).

Asymptotic equivalence between two linear volterra difference systems

Abstract We study asymptotic equivalence between the solutions of linear Volterra difference system x(n+1)=A(n)x(n)+ ∑ s=n 0 n B(n,s)x(s) and its perturbed system y(n+1)=A(n)y(n)+ ∑ s=n 0 n B(n,s)y(s)+F(n)

Asymptotic property in variation for nonlinear differential systems

For nonlinear differential systems, we investigate that the two concepts of the asymptotic equivalence and asymptotic equivalence in variation are equivalent under the conditions of strong stability and t∞-similarity, and give some examples.

The oscillation of partial difference equations with continuous arguments

Abstract For the partial difference equations and we shall obtain sufficient conditions for the oscillation of all solutions of these equations.

ASYMPTOTIC BEHAVIOR OF NONLINEAR VOLTERRA DIFFERENCE SYSTEMS

We study the asymptotic behavior of nonlinear Volterra difference system x(n + 1) = f(n, x(n)) + n ∑ s=n0 g(n, s, x(s)), x(n0) = x0 by using the resolvent matrix R(n, m) of the corresponding linear Volterra system and the comparison principle.

ASYMPTOTIC EQUIVALENCE BETWEEN LINEAR DIFFERENTIAL SYSTEMS

We study the strong stability for linear difierential sys- tems in connection with t1-similarity, and investigate the asymp- totic equivalence between linear difierential systems.

h-STABILITY OF PERTURBED VOLTERRA DIFFERENCE SYSTEMS

We discuss the h-stability of perturbed Volterra dif- ference systems by means of the resolvent matrix and discrete in- equalities.