Delay equations and nonuniform exponential stability

Luis Barreira; Claudia Valls

doi:10.3934/dcdss.2008.1.219

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2008, Volume 1, Issue 2: 219-223. Doi: 10.3934/dcdss.2008.1.219

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Delay equations and nonuniform exponential stability

Luis Barreira^1, and
Claudia Valls^2,

1.
Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa
2.
Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa

Received: June 30, 2007

Revised: October 31, 2007

Published: May 2008

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Abstract

For nonautonomous linear delay equations $v'=L(t)v_t$ admitting a nonuniform exponential contraction, we establish the nonuniform exponential stability of the equation $v'=L(t) v_t +f(t,v_t)$ for a large class of nonlinear perturbations.

Keywords:

Delay equations,
nonuniform exponential stability.

Mathematics Subject Classification: Primary: 34K20.

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