Existence and roughness of the exponential dichotomy for skew-product semiflow in Banach spaces
From MaRDI portal
Publication:1896768
DOI10.1006/jdeq.1995.1117zbMath0831.34067OpenAlexW2037508501MaRDI QIDQ1896768
Publication date: 11 September 1995
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jdeq.1995.1117
Nonlinear differential equations in abstract spaces (34G20) Asymptotic properties of solutions to ordinary differential equations (34D05)
Related Items
Exponential dichotomy and \((\ell^p,\ell^q)\)-admissibility on the half-line, A Zabczyk type method for the study of the exponential trichotomy of discrete dynamical systems, Stable invariant manifolds with impulses and growth rates, On stability of discrete dynamical systems: from global methods to ergodic theory approaches, Exponential instability of linear skew-product semiflows in terms of Banach function spaces, Robustness for stable impulsive equations via quadratic Lyapunov functions, Uniform and strict persistence in monotone skew-product semiflows with applications to non-autonomous Nicholson systems, Uniformly \(rd\)-piecewise almost periodic functions with applications to the analysis of impulsive \(\Delta\)-dynamic system on time scales, Pointwise trichotomy for skew-evolution semiflows on Banach spaces, Robustness for impulsive equations, Approximate controllability of discrete semilinear systems and applications, Exponential trichotomy and \(p\)-admissibility for evolution families on the real line, A version of a theorem of R. Datko for stability in average, Globally positive solutions of linear parabolic PDEs of second order with Robin boundary conditions, Equivalences between nonuniform exponential dichotomy and admissibility, General exponential dichotomies on time scales and parameter dependence of roughness, Nonuniform input-output criteria for exponential expansiveness of discrete dynamical systems and applications, New criteria for exponential expansiveness of variational difference equations, Discrete-time theorems for global and pointwise dichotomies of cocycles over semiflows, Transversality of homoclinic orbits and exponential dichotomies for parabolic equations, Global and cocycle attractors for non-autonomous reaction-diffusion equations. The case of null upper Lyapunov exponent, Spectral theory for general nonautonomous/random dispersal evolution operators, Admissibility criteria for nonuniform dichotomic behavior of nonautonomous systems on the whole line, Robustness of the exponential dichotomies of boundary-value problems for the general first-order hyperbolic systems, Classical bounded and almost periodic solutions to quasilinear first-order hyperbolic systems in a strip, Robustness of nonuniform behavior for discrete dynamics, Admissibility and nonuniform exponential dichotomy on the half-line, Exponential dichotomy for asymptotically hyperbolic two-dimensional linear systems, Exponential behavior in Banach spaces: robustness of trichotomies in discrete time, Admissibility and exponential trichotomy of dynamical systems described by skew-product flows, On spectral characterization of nonuniform hyperbolicity, Necessary and sufficient criteria for the existence of exponential dichotomy on time scales, A generalized nonuniform contraction and Lyapunov function, Construction of quasi-periodic solutions of state-dependent delay differential equations by the parameterization method. I: Finitely differentiable, hyperbolic case, Minimal sets in monotone and concave skew-product semiflows. I: A general theory, Perturbation theory for the approximation of stability spectra by QR methods for sequences of linear operators on a Hilbert space, On the robustness of nonuniform exponential trichotomies, Lyapunov functions for general nonuniform dichotomies, Existence of global attractor for a nonautonomous state-dependent delay differential equation of neuronal type, An a posteriori KAM theorem for whiskered tori in Hamiltonian partial differential equations with applications to some ill-posed equations, An ergodic theorem in the qualitative behavior of (non)linear semiflows, Robustness of nonuniform exponential dichotomies in Banach spaces, Robustness of nonuniform \((\mu , \nu )\)-dichotomies in Banach spaces, Exponential dichotomy and dichotomy radius for difference equations, Approaching the discrete dynamical systems by means of skew-evolution semiflows, Evolution semigroups, translation algebras, and exponential dichotomy of cocycles, New conditions for (non)uniform behaviour of linear cocycles over flows, Robust stability and stability radius for variational control systems, Nonuniform mean-square exponential dichotomies and mean-square exponential stability, Input-output criteria for stability and expansiveness of dynamical systems, A general framework for splitting concepts for cocycles over generalized nonautonomous dynamical systems, Robustness of a weaker notion of exponential dichotomy, Stability of difference equations and applications to robustness problems, Input-output admissibility and exponential trichotomy of difference equations, Translation invariant spaces and asymptotic properties of variational equations, Integral equations and exponential trichotomy of skew-product flows, Integral conditions for exponential dichotomy: a nonlinear approach, Skew-product semi-flows and non-autonomous control systems, Robustness of dichotomies and trichotomies for difference equations, Nonlinear criteria for the existence of the exponential trichotomy in infinite dimensional spaces, Exponential stability for linear skew-product flows, Smooth robustness of parameterized perturbations of exponential dichotomies, Optimal regularity of robustness for parameterized perturbations, Robust nonuniform dichotomies and parameter dependence, Schäffer spaces and uniform exponential stability of linear skew-product semiflows, The effect of a small bounded noise on the hyperbolicity for autonomous semilinear differential equations, \((L^p(\mathbb R_+,X),L^q(\mathbb R_+,X))\)-admissibility and exponential dichotomies of cocycles, Existence and roughness of exponential dichotomies of linear dynamic equations on time scales, Hyperbolicity via evolution semigroups on \(L^p\), General exponential dichotomies: from finite to infinite time, On uniform exponential trisplitting of discrete skew-product semiflows, Non-wandering points for autonomous/periodic parabolic equations on the circle, On the asymptotic behavior of discrete dynamical systems -- an ergodic theory approach, The weak Smale horseshoe and mean hyperbolicity, Robustness of hyperbolicity in delay equations, Robustness of exponential dichotomies in mean, Strong exponential dichotomy of discrete nonautonomous systems: input-output criteria and strong dichotomy radius, Robustness via Lyapunov functions, Admissibility in the strong and weak senses, Global attractivity in concave or sublinear monotone infinite delay differential equations, Nonuniform behavior and robustness, Robustness for linear evolution equations with non-instantaneous impulsive effects, On the scaling limits at zeros of solutions of parabolic equations, Exponential dichotomy and admissibility of linearized skew-product semiflows defined on a compact positively invariant subset of semiflows, Robustness of general dichotomies, Non-Atkinson perturbations of nonautonomous linear Hamiltonian systems: exponential dichotomy and nonoscillation, Discretized characterizations of exponential dichotomy of linear skew-product semiflows over semiflows, On dichotomous behavior of variational difference equations and applications, Barbashin-type conditions for exponential stability of linear cocycles, Lyapunov functions for trichotomies with growth rates, Robustness of discrete dynamics via Lyapunov sequences, Criterions for detecting the existence of the exponential dichotomies in the asymptotic behavior of the solutions of variational equations, Invariant foliations for parabolic equations, Quaternionic exponentially dichotomous operators through \(S\)-spectral splitting and applications to Cauchy problem, Exponential dichotomy of difference equations and applications to evolution equations on the half-line, Exponential forward splitting for noninvertible difference equations, Parabolic differential equations with bounded delay, Evolution maps for delay-difference equations, Persistence of exponential trichotomy for linear operators: a Lyapunov-Perron approach, Exponential dichotomy and existence of almost periodic solutions of impulsive differential equations, Exponential stability for nonautonomous functional differential equations with state-dependent delay, Lyapunov and dynamical spectra for Banach state-spaces, Existence and robustness of exponential dichotomy of linear skew-product semiflows over semiflows, Admissibility and roughness of nonuniform exponential dichotomies for difference equations, Exponential behavior in mean for cocycles, Lyapunov functions for strong exponential contractions, Nonuniform \((h,k,\mu,\nu)\)-dichotomy with applications to nonautonomous dynamical systems, Nonuniform \(\mu \)-dichotomy spectrum and kinematic similarity, Splitting with different growth rates for linear discrete-time skew-evolution semiflows in Banach spaces, Input-output criteria for the trichotomic behaviors of discrete dynamical systems, New class of perturbations for nonuniform exponential dichotomy roughness, On tempered exponential trisplitting for random semi-dynamical systems, Induced delay equations, Is the Sacker–Sell type spectrum equal to the contractible set?, Robustness of nonuniform mean-square exponential dichotomies, Exact controllability for semilinear difference equation and application, Existence and roughness of nonuniform exponential dichotomies on time scales, One admissible critical pair without Lyapunov norm implies a tempered exponential dichotomy for Met-systems, Perron type theorems for skew-evolution semiflows, Approximating Lyapunov exponents and Sacker-Sell spectrum for retarded functional differential equations, AFFINE-PERIODIC SOLUTIONS AND PSEUDO AFFINE-PERIODIC SOLUTIONS FOR DIFFERENTIAL EQUATIONS WITH EXPONENTIAL DICHOTOMY AND EXPONENTIAL TRICHOTOMY, Discrete admissibility and exponential trichotomy of dynamical systems, Topological dynamics for monotone skew-product semiflows with applications, Two definitions of exponential dichotomy for skew-product semiflow in Banach spaces, Asymptotic stability of nonuniform behaviour, Dynamical spectrum for scalar parabolic equations, Hyperbolicity via admissibility in delay equations, Hyperbolicity of delay equations via cocycles, Exponential dichotomy of difference equations in \(l_{p}\)-phase spaces on the half-line, Input–output control systems and dichotomy of variational difference equations, Hyers–Ulam stability for hyperbolic random dynamics, Stability and Stabilizability for Linear Systems of Difference Equations, Exponential dichotomies with respect to a sequence of norms and admissibility, Exponential dichotomy for evolution families on the real line, Nonuniform exponential stability and admissibility, Exponential dichotomies of impulsive dynamic systems with applications on time scales, Exponential Expansiveness and Complete Admissibility For Evolution Families, Robustness of nonuniform exponential trichotomies in Banach spaces, Smooth robustness of exponential dichotomies, Exponential trichotomy for variational difference equations, Almost Periodic Solutions of Evolution Differential Equations with Impulsive Action, Unnamed Item, The Selgrade decomposition for linear semiflows on Banach spaces, Robustness of noninvertible dichotomies, Admissibility for exponential dichotomies in average, Relative asymptotic equivalence between difference equations, Characterization of strong exponential dichotomies, Permanence of nonuniform nonautonomous hyperbolicity for infinite-dimensional differential equations