Solution estimates for nonlinear nonautonomous evolution equations in spaces with normalizing mappings

M. I. Gil'

doi:10.1023/A:1012731022634

Solution estimates for nonlinear nonautonomous evolution equations in spaces with normalizing mappings

M. I. Gil'

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Nonlinear nonautonomous evolution equations in a space with a normalizing mapping (a generalized norm) are considered. Solution estimates are established. In particular cases these estimates generalize the Wazewski and Lozinskii estimates from the theory of ordinary differential equations. By the obtained estimates, the following problems are investigated: asymptotic stability, boundedness of solutions, input-output stability, existence of periodic solutions. Applications to integro-differential equations are discussed.

Original language	English
Pages (from-to)	1-23
Number of pages	23
Journal	Acta Applicandae Mathematicae
Volume	69
Issue number	1
DOIs	https://doi.org/10.1023/A:1012731022634
State	Published - 1 Oct 2001

Keywords

Asymptotic stability
Boundedness of solutions
Input-output stability
Integro-differential equations
Nonlinear evolution equations
Periodic solutions

ASJC Scopus subject areas

Applied Mathematics

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abstract = "Nonlinear nonautonomous evolution equations in a space with a normalizing mapping (a generalized norm) are considered. Solution estimates are established. In particular cases these estimates generalize the Wazewski and Lozinskii estimates from the theory of ordinary differential equations. By the obtained estimates, the following problems are investigated: asymptotic stability, boundedness of solutions, input-output stability, existence of periodic solutions. Applications to integro-differential equations are discussed.",

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AB - Nonlinear nonautonomous evolution equations in a space with a normalizing mapping (a generalized norm) are considered. Solution estimates are established. In particular cases these estimates generalize the Wazewski and Lozinskii estimates from the theory of ordinary differential equations. By the obtained estimates, the following problems are investigated: asymptotic stability, boundedness of solutions, input-output stability, existence of periodic solutions. Applications to integro-differential equations are discussed.

KW - Asymptotic stability

KW - Boundedness of solutions

KW - Input-output stability

KW - Integro-differential equations

KW - Nonlinear evolution equations

KW - Periodic solutions

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ER -

Solution estimates for nonlinear nonautonomous evolution equations in spaces with normalizing mappings

Abstract

Keywords

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