Abstract
In this paper, we investigate many types of stability, like uniform stability, asymptotic stability, uniform asymptotic stability, global stability, global asymptotic stability, exponential stability, uniform exponential stability, of the homogeneous first-order linear dynamic equations of the form x � (t )= Ax(t), t > t0, t, t0 ∈ T x(t0 )= x0 ∈ D(A),
Highlights
Introduction and preliminariesThe history of asymptotic stability of dynamic equations on a time scale goes back to Aulbach and Hilger [ ]
For a real scalar dynamic equation, stability and instability results were obtained by Gard and Hoffacker [ ]
The theory of dynamic equations on time scales was introduced by Stefan Hilger in [ ], in order to unify continuous and discrete calculus [, ]
Summary
Introduction and preliminariesThe history of asymptotic stability of dynamic equations on a time scale goes back to Aulbach and Hilger [ ]. 2 The existence and uniqueness of solutions of dynamic equations Our aim is to prove that the first order initial value problem x (t) = Ax(t), t ∈ T, x( ) = x ∈ D(A)
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