The dichotomy theorem for evolution bi-families
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Publication:949635
DOI10.1016/j.jde.2008.01.023zbMath1154.47010OpenAlexW2125310703MaRDI QIDQ949635
Publication date: 21 October 2008
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jde.2008.01.023
(Semi-) Fredholm operators; index theories (47A53) Linear differential equations in abstract spaces (34G10) Operator sine and cosine functions and higher-order Cauchy problems (47D09)
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Cites Work
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- On invertibility and the Fredholm property of parabolic differential operators
- Krein's formula for indefinite multipliers in linear periodic Hamiltonian systems
- Relative morse indices, Fredholm indices, and group velocities
- On differential and difference Fredholm operators
- Exponential dichotomies and homoclinic orbits in functional differential equations
- A reduction principle for nonautonomous systems in infinite-dimensional spaces
- The splitting index for linear differential systems
- Geometric theory of semilinear parabolic equations
- Hamiltonian and Lagrangian flows on center manifolds with applications to elliptic variational problems
- Invertibility and dichotomy of differential operators on a half-line
- Exponential stability, exponential expansiveness, and exponential dichotomy of evolution equations on the half-line
- The Fredholm alternative for functional-differential equations of mixed type
- Exponential dichotomies for solitary-wave solutions of semilinear elliptic equations on infinite cylinders
- Ordinary differential operators in Hilbert spaces and Fredholm pairs
- Fredholm differential operators with unbounded coefficients
- Wave-solutions of reversible systems and applications
- Exponential dichotomies and transversal homoclinic points
- On the Structure of Spectra of Modulated Travelling Waves
- Exponential Dichotomies and Fredholm Operators
- Spectral asymmetry and Riemannian geometry. III
- Exponential dichotomies for linear non-autonomous functional differential equations of mixed type
- Propagation of hexagonal patterns near onset
- On Fredholm properties of Lu = u′ − A(t)u for paths of sectorial operators
- On correct linear differential operators
- Morse homology on Hilbert spaces
- The Spectral Flow and the Maslov Index
- Pattern formation outside of equilibrium
- Integral Operators and the Compactness of Induced Representations
- Optimal regularity and Fredholm properties of abstract parabolic operators in $L^{p}$ spaces on the real line
- Characterizations of dichotomies of evolution equations on the half-line
