Exponential dichotomy of linear impulsive differential equations in a Banach space

Nonlinear Impulsive Differential Equations with Weighted Exponential or Ordinary Dichotomous Linear Part in a Banach Space

“…∈ we obtain the notion exponential and ordinary dichotomy for impulsive differential equations considered in [3,20,21]. That is why our main results in this paper appear as a generalization of some results there.…”

“…As shown, for instance in [3,4], if the operators have bounded inverse ones, then for the impulsive linear equation (3), (4) there exists a Cauchy operator ( ), ( ∈ ) by means of which each solution ( ) of (3), (4) for which ( ) = ∈ has the form…”

“…(1) The linear impulsive differential equation (3), (4) (1), (2) has for each ∈ 1 = 1 with | (0) | ≤ a unique solution ( ) on + for which 1 (0) = and | ( ) ( )| ≤ ( ∈ R + ).…”

“…The qualitative investigation of these processes began with the work of Mil'man and Myshkis [1]. For the first time such equations were considered in an arbitrary Banach space in [2][3][4][5].…”

Exponential dichotomy of difference equations in lp-phase spaces on the half-line

“…This means that one can drop the above priori condition in the case that the difference equations are defined on Z (see [7,Theorem 3.3] for the original result and see also [2,3,11,15] for recent results on the exponential dichotomy of difference equations defined on Z).…”