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Part A Introduction
Continuoxxs dependence of the solutions on an initial condition
General exponents of impulsive differential equations
Analogously asymptotically stable ball Banach space bounded inverse operators bounded operators bounded solution Cauchy operator Cauchy problem CB(R+,X conditions H16 conditions of Theorem Corollary defined Definition differential equation 6.1 direct sum equation dx estimate is valid evolution operator exist a number exist constants exponent exponential dichotomy exponentially dichotomous following conditions hold following equality following estimate following inequality follows the existence follows the inequality formula function f function F(t,x function x(t Gronwall's lemma Hence homeomorphism homogeneous equation impulse effect impulsive differential equation impulsive equation inequality is valid initial value integral manifold interval last inequality Let the conditions Let the following linear equation maps Moreover Morse lemma obtain the estimate operator Q operator-function A(t ordinary differential equation positive constants projectors Qnx(tn respectively satisfy the condition say that conditions solution x(t spectral sets subspaces sufficiently small values Theorem 6.8 topologically equivalent x(t+