Differential and Integral Equations

Nonautonomous delay differential equations in Hilbert spaces and Lyapunov exponents

Dimitri Breda

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A general class of linear and nonautonomous delay differential equations with initial data in a separable Hilbert space is treated. The classic questions of existence, uniqueness, and regularity of solutions are addressed. Moreover, the semigroup approach typically adopted in the autonomous case for continuous initial functions is extended, and thus the existence of an equivalent abstract ordinary formulation is shown to hold. Finally, the existence of infinitely many Lyapunov exponents for the associated evolution is proven and their meaning is discussed.

Article information

Differential Integral Equations, Volume 23, Number 9/10 (2010), 935-956.

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions 34K06: Linear functional-differential equations 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx] 37H15: Multiplicative ergodic theory, Lyapunov exponents [See also 34D08, 37Axx, 37Cxx, 37Dxx]


Breda, Dimitri. Nonautonomous delay differential equations in Hilbert spaces and Lyapunov exponents. Differential Integral Equations 23 (2010), no. 9/10, 935--956. https://projecteuclid.org/euclid.die/1356019118

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