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Zeitschrift für Analysis und ihre Anwendungen


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Volume 12, Issue 2, 1993, pp. 361–378
DOI: 10.4171/ZAA/559

Published online: 1993-06-30

About Integral Equivalence between Linear and Nonlinear Operator Impulsive Differential Equations in a Banach Space

S.I. Kostadinov[1] and Dieter Schott[2]

(1) University of Plovdiv, Bulgaria
(2) Hochschule Wismar, Germany

After an introduction into the problems of impulsive operator differential equations sufficient conditions for the integral and the asymptotic equivalence between linear and nonlinear equations of this kind are presented. These conditions guarantee that for bounded solutions of the linear equation there are also bounded solutions of the corresponding nonlinear equation.

Keywords: Abstract impulsive differential equations, integral equivalence, asymptotic equivalence, exponential dichotomy, fixed point theorem of Schauder

Kostadinov S.I., Schott Dieter: About Integral Equivalence between Linear and Nonlinear Operator Impulsive Differential Equations in a Banach Space. Z. Anal. Anwend. 12 (1993), 361-378. doi: 10.4171/ZAA/559