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Exponential dichotomy and invariant manifolds of semi-linear differential equations on the line.
- Source :
- Studia Universitatis Babeş-Bolyai, Mathematica; Mar2024, Vol. 69 Issue 1, p127-148, 22p
- Publication Year :
- 2024
-
Abstract
- In this paper we investigate the homogeneous linear differential equation v'(t) = A(t)v(t) and the semi-linear differential equation v'(t) = A(t)v(t) + g(t, v(t)) in Banach space X, in which A: R → L(X) is a strongly continuous function, g: R × X → X is continuous and satisfies φ-Lipschitz condition. The first we characterize the exponential dichotomy of the associated evolution family with the homogeneous linear differential equation by space pair (E, E1), this is a Perron type result. Applying the achieved results, we establish the robustness of exponential dichotomy. The next we show the existence of stable and unstable manifolds for the semi-linear differential equation and prove that each a fiber of these manifolds is differentiable submanifold of class C¹. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02521938
- Volume :
- 69
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Studia Universitatis Babeş-Bolyai, Mathematica
- Publication Type :
- Academic Journal
- Accession number :
- 176575966
- Full Text :
- https://doi.org/10.24193/subbmath.2024.1.09