Uniform dichotomy and exponential dichotomy of evolution families on the half-line

DOI10.1016/j.jmaa.2005.12.002zbMath1113.34038OpenAlexW2014202711MaRDI QIDQ855465

Bogdan Sasu

Publication date: 7 December 2006

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2005.12.002

zbMATH Keywords

integral equationexponential dichotomyevolution familydifference equationuniform dichotomydiscrete evolution family

Mathematics Subject Classification ID

Discrete version of topics in analysis (39A12) Linear differential equations in abstract spaces (34G10) Dichotomy, trichotomy of solutions to ordinary differential equations (34D09)

Related Items (19)

Exponential trichotomy and \((r, p)\)-admissibility for discrete dynamical systems ⋮ Nonuniform exponential dichotomy for discrete dynamical systems in Banach spaces ⋮ A functional-analytical approach to the asymptotics of recursions ⋮ Equivalences between nonuniform exponential dichotomy and admissibility ⋮ New criteria for exponential expansiveness of variational difference equations ⋮ Admissibility criteria for nonuniform dichotomic behavior of nonautonomous systems on the whole line ⋮ Admissibility and nonuniform exponential dichotomy on the half-line ⋮ Almost Periodicity for a Nonautonomous Discrete Dispersive Population Model ⋮ Existence and roughness of nonuniform exponential dichotomies on time scales ⋮ Discrete admissibility and exponential trichotomy of dynamical systems ⋮ Approaching the discrete dynamical systems by means of skew-evolution semiflows ⋮ Input–output control systems and dichotomy of variational difference equations ⋮ Exponential dichotomies of evolution operators in Banach spaces ⋮ Pairs of function spaces and exponential dichotomy on the real line ⋮ Input-output admissibility and exponential trichotomy of difference equations ⋮ Integral equations, dichotomy of evolution families on the half-line and applications ⋮ Exponential dichotomy on time scales and admissibility of the pair \((\mathrm{C}_{\mathrm{rd}}^{b}(\mathbb{T}^{+}, X),L^{p}(\mathbb{T}^{+},X))\) ⋮ On dichotomous behavior of variational difference equations and applications ⋮ On exponential dichotomy of variational difference equations

Cites Work

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• Exponential dichotomy and \((\ell^p,\ell^q)\)-admissibility on the half-line
• Exponential trichotomy and \(p\)-admissibility for evolution families on the real line
• Dichotomies in stability theory
• Exponential stability, exponential expansiveness, and exponential dichotomy of evolution equations on the half-line
• On nonuniform exponential dichotomy of evolution operators in Banach spaces.
• Discrete admissibility and exponential dichotomy for evolution families
• Input-output conditions for the asymptotic behavior of linear skew-product flows and applications
• Dichotomies for linear difference equations
• New characterizations of exponential dichotomy and exponential stability of linear difference equations
• Characterizations of dichotomies of evolution equations on the half-line

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