Abstract Impulsive Differential Equations |
Contents
Part A Introduction | 1 |
Continuous dependence of the solutions on an initial condition | 11 |
Nonlinear equations | 32 |
Copyright | |
11 other sections not shown
Common terms and phrases
Analogously arbitrary asymptotically stable Banach space bounded functions bounded solution Cauchy problem CB(R+ conditions of Theorem Consider defined denote equation 9.1 equation dx dt estimate is valid evolution operator exist a number exist constants exponent exponentially dichotomous following conditions hold following equality following estimate following inequality follows the estimate follows the existence follows the inequality formula function F(t hard to check Hence homeomorphism impulse effect impulsive differential equation impulsive equation inequality is valid initial value initial value problem integral manifold interval kinematically similar Let the conditions Let the following linear equation Moreover N₁ nonhomogeneous nonlinear obtain the estimate operator Q operator-function A(t ordinary differential equation P₁ projectors Qnx(tn relatively compact respectively S(R+ satisfies the condition sequence solution x(t subspace sufficiently small values tn+1 topologically equivalent uniformly W₁(t W₂(t X₁ Y(tn y₁