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- Title
Dichotomy of solutions of functional-differential equations in the Sobolev space.
- Authors
Romanovskii, R.; Nazaruk, E.
- Abstract
For a linear system of functional-differential equations of delay type, by the Lyapunov direct method, we prove a sufficient criterion for exponential dichotomy in the H-topology in terms of operator inequalities. The original problem is reduced to the same problem for a difference equation of the form u = Λ u in the state space H(0, 1) with compact operator Λ. Subspaces realizing the dichotomy are constructed. The constructions are carried out in a basis taking into account the specific properties of the space H and coordinated with the metric chosen in it. An illustrative example is considered.
- Subjects
SOBOLEV spaces; NUMERICAL solutions to functional differential equations; LYAPUNOV exponents; DIFFERENTIAL inequalities; OPERATOR equations
- Publication
Differential Equations, 2015, Vol 51, Issue 4, p464
- ISSN
0012-2661
- Publication type
Article
- DOI
10.1134/S0012266115040047