AMBIENTUM BIOETHICA BIOLOGIA CHEMIA DIGITALIA DRAMATICA EDUCATIO ARTIS GYMNAST. ENGINEERING EPHEMERIDES EUROPAEA GEOGRAPHIA GEOLOGIA HISTORIA HISTORIA ARTIUM INFORMATICA IURISPRUDENTIA MATHEMATICA MUSICA NEGOTIA OECONOMICA PHILOLOGIA PHILOSOPHIA PHYSICA POLITICA PSYCHOLOGIA-PAEDAGOGIA SOCIOLOGIA THEOLOGIA CATHOLICA THEOLOGIA CATHOLICA LATIN THEOLOGIA GR.-CATH. VARAD THEOLOGIA ORTHODOXA THEOLOGIA REF. TRANSYLVAN
|
|||||||
Rezumat articol ediţie STUDIA UNIVERSITATIS BABEŞ-BOLYAI În partea de jos este prezentat rezumatul articolului selectat. Pentru revenire la cuprinsul ediţiei din care face parte acest articol, se accesează linkul din titlu. Pentru vizualizarea tuturor articolelor din arhivă la care este autor/coautor unul din autorii de mai jos, se accesează linkul din numele autorului. |
|||||||
STUDIA MATHEMATICA - Ediţia nr.1 din 2024 | |||||||
Articol: |
EXPONENTIAL DICHOTOMY AND INVARIANT MANIFOLDS OF SEMI-LINEAR DIFFERENTIAL EQUATIONS ON THE LINE. Autori: TRINH VIET DUOC, NGUYEN NGOC HUY. |
||||||
Rezumat: DOI: 10.24193/subbmath.2024.1.09 Received 19 September 2021; Accepted 20 January 2022. Published Online: 2024-03-20 Published Print: 2024-03-30 pp. 127-148 VIEW PDF FULL PDF In this paper we investigate the homogeneous linear differential equation v0(t) = A(t)v(t) and the semi-linear differential equation v0(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. Mathematics Subject Classification (2010): 34C45, 34D09, 34D10. |
|||||||