Generalized Aizerman-Myshkis problem for abstract differential-delay equations

M. I. Gil

doi:10.1016/j.na.2003.07.017

Generalized Aizerman-Myshkis problem for abstract differential-delay equations

M. I. Gil

Department of Mathematics

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

6 Scopus citations

Abstract

We consider a class of semilinear functional-differential equations in a Hilbert space. Conditions for the absolute stability are established. Moreover, it is shown that these conditions separate equations that satisfy the generalized Aizerman-Myshkis hypothesis. The suggested approach is based on a combined usage of the properties of operators on tensor products of Hilbert spaces and recent estimates for the norm of the resolvent. Our results are new even in the finite-dimensional case. We also discuss applications of the mentioned results to coupled systems of parabolic equations with delay and integro-differential equations with delay.

Original language	English
Pages (from-to)	771-784
Number of pages	14
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	55
Issue number	6
DOIs	https://doi.org/10.1016/j.na.2003.07.017
State	Published - 1 Dec 2003

Keywords

Absolute stability
Abstract nonlinear differential-delay equations
Tensor products
The Aizerman-Myshkis problem

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2003.07.017

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title = "Generalized Aizerman-Myshkis problem for abstract differential-delay equations",

abstract = "We consider a class of semilinear functional-differential equations in a Hilbert space. Conditions for the absolute stability are established. Moreover, it is shown that these conditions separate equations that satisfy the generalized Aizerman-Myshkis hypothesis. The suggested approach is based on a combined usage of the properties of operators on tensor products of Hilbert spaces and recent estimates for the norm of the resolvent. Our results are new even in the finite-dimensional case. We also discuss applications of the mentioned results to coupled systems of parabolic equations with delay and integro-differential equations with delay.",

keywords = "Absolute stability, Abstract nonlinear differential-delay equations, Tensor products, The Aizerman-Myshkis problem",

author = "Gil, \{M. I.\}",

note = "Funding Information: This research was in supported by the Kamea Fund. ",

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T1 - Generalized Aizerman-Myshkis problem for abstract differential-delay equations

AU - Gil, M. I.

N1 - Funding Information: This research was in supported by the Kamea Fund.

PY - 2003/12/1

Y1 - 2003/12/1

N2 - We consider a class of semilinear functional-differential equations in a Hilbert space. Conditions for the absolute stability are established. Moreover, it is shown that these conditions separate equations that satisfy the generalized Aizerman-Myshkis hypothesis. The suggested approach is based on a combined usage of the properties of operators on tensor products of Hilbert spaces and recent estimates for the norm of the resolvent. Our results are new even in the finite-dimensional case. We also discuss applications of the mentioned results to coupled systems of parabolic equations with delay and integro-differential equations with delay.

AB - We consider a class of semilinear functional-differential equations in a Hilbert space. Conditions for the absolute stability are established. Moreover, it is shown that these conditions separate equations that satisfy the generalized Aizerman-Myshkis hypothesis. The suggested approach is based on a combined usage of the properties of operators on tensor products of Hilbert spaces and recent estimates for the norm of the resolvent. Our results are new even in the finite-dimensional case. We also discuss applications of the mentioned results to coupled systems of parabolic equations with delay and integro-differential equations with delay.

KW - Absolute stability

KW - Abstract nonlinear differential-delay equations

KW - Tensor products

KW - The Aizerman-Myshkis problem

UR - https://www.scopus.com/pages/publications/0142106989

U2 - 10.1016/j.na.2003.07.017

DO - 10.1016/j.na.2003.07.017

M3 - Article

AN - SCOPUS:0142106989

SN - 0362-546X

VL - 55

SP - 771

EP - 784

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 6

ER -

Generalized Aizerman-Myshkis problem for abstract differential-delay equations

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Keywords

ASJC Scopus subject areas

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