An extension of some theorems of L. Barreira and C. Valls for the nonuniform exponential dichotomous evolution operators

DOI10.1016/j.jmaa.2011.10.062zbMath1242.34114OpenAlexW1997254959MaRDI QIDQ663660

Cristina Praţa, Ciprian Preda, Petre Preda

Publication date: 27 February 2012

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.2011.10.062

zbMATH Keywords

admissibilitynonuniformly exponential boundednessnonuniformly exponential dichotomystrongly continuous evolution family

Mathematics Subject Classification ID

Nonlinear differential equations in abstract spaces (34G20) Dichotomy, trichotomy of solutions to ordinary differential equations (34D09)

Related Items (7)

Nonuniform exponential dichotomy for linear skew-product semiflows over semiflows ⋮ Nonuniform \((h,k,\mu,\nu)\)-dichotomy with applications to nonautonomous dynamical systems ⋮ Extending some results of L. Barreira and C. Valls to the case of linear skew-product semiflows ⋮ Exponential stability concepts for evolution families on \(\mathbb{R}\) ⋮ Admissibility for nonuniform \((\mu,v)\) contraction and dichotomy ⋮ NONLINEAR PERTURBATIONS FOR LINEAR NONAUTONOMOUS IMPULSIVE DIFFERENTIAL EQUATIONS AND NONUNIFORM (<i>H,K,µ,ν</i>)-DICHOTOMY ⋮ Nonuniform exponential dichotomy for evolution families on the real line

Cites Work

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• Nonuniform exponential dichotomies and admissibility
• Admissibility for nonuniform exponential contractions
• Schäffer spaces and exponential dichotomy for evolutionary processes
• Invariant manifolds of admissible classes for semi-linear evolution equations
• Stable manifolds for semi-linear evolution equations and admissibility of function spaces on a half-line
• Nonuniform exponential contractions and Lyapunov sequences
• Semigroups of linear operators and applications to partial differential equations
• Invertibility and dichotomy of differential operators on a half-line
• Infinite dimensional linear systems theory
• Exponential dichotomy and mild solutions of nonautonomous equations in Banach spaces
• Exponential stability, exponential expansiveness, and exponential dichotomy of evolution equations on the half-line
• Hyperbolic evolution semigroups on vector valued function spaces
• An integrability condition on the resolvent for hyperbolicity of the semigroup
• Exponential dichotomy of difference equations and applications to evolution equations on the half-line
• Schäffer spaces and uniform exponential stability of linear skew-product semiflows
• Exponentially dichotomous operators and exponential dichotomy of evolution equations on the half-line
• \((L^p,L^q)\)-admissibility and exponential dichotomy of evolutionary processes on the half-line
• Evolutionary semigroups and Lyapunov theorems in Banach spaces
• Dichotomy of differential equations on Banach spaces and an algebra of weighted translation operators
• The spectral mapping theorem for evolution semigroups on spaces of vector-valued functions
• Sets of ``non-typical points have full topological entropy and full Hausdorff dimension
• Nonuniform exponential dichotomies and Lyapunov regularity
• Stability of nonautonomous differential equations
• Exponential dichotomy of evolution equations and admissibility of function spaces on a half-line
• Optimal estimates along stable manifolds of non-uniformly hyperbolic dynamics
• Nonuniform dichotomy of evolutionary processes in Banach spaces
• On the proof of characterizations of the exponential dichotomy
• Semigroups and Stability of Nonautonomous Differential Equations in Banach Spaces
• Sufficient conditions for exponential stability and dichotomy of evolution equations
• Asymptotically autonomous parabolic evolution equations.
• Characterizations of dichotomies of evolution equations on the half-line

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