h-STABILITY AND BOUNDEDNESS IN THE PERTURBED FUNCTIONAL DIFFERENTIAL SYSTEMS

Abstract

Abstract. In this paper, we investigate h-stability and bounds for solutions of the the functional perturbed differential systems.

Boundedness in Nonlinear Perturbed Differential Systems

“…Theorem 3.1. Suppose that f x (t, 0) is t ∞ -similar to f x (t, x(t, t 0 , x 0 )) for t ≥ t 0 ≥ 0 and |x 0 | ≤ δ for some constant δ > 0, the solution x = 0 of (1) is hS with a positive continuous function h, and g in (9)…”

“…The weak condition of a function h and the strong condition of a function g in Theorem 3.3 [8] are the following result. x(t, t 0 , x 0 )) for t ≥ t 0 ≥ 0 and |x 0 | ≤ δ for some constant δ > 0, the solution x = 0 of (1) is hS with a positive continuous function h, and g in (9)…”

Boundedness in the Nonlinear Functional Differential Systems

“…Choi, Ryu [5] and Choi, Koo, and Ryu [4] investigated bounds of solutions for nonlinear perturbed systems. Also, Goo [7,8,9,10] and Goo et al [2,3,11] investigated boundedness of solutions for nonlinear perturbed systems.…”