On Bounded Solutions of Systems of Linear Functional Differential Equations
نویسنده
چکیده
Sufficient conditions of the existence and uniqueness of bounded on real axis solutions of systems of linear functional differential equations are established. 1. Formulations of the Main Results Let R be the set of real numbers, Cloc(R, R) be the space of continuous functions u : R → R with the topology of uniform convergence on every compact interval and Lloc(R,R) be the space of locally summable functions u : R → R with the topology of convergence in the mean on every compact interval. Consider the system of functional differential equations x′ i(t) = n ∑ k=1 lik(xk)(t) + qi(t) (i = 1, . . . , n), (1.1) where lik : Cloc(R,R) → Lloc(R, R) (i, k = 1, . . . , n) are linear continuous operators and qi ∈ Lloc(R, R) (i = 1, . . . , n). Moreover, there exist linear positive operators lik : Cloc(R,R) → Lloc(R,R) (i, k = 1, . . . , n) such that for any u ∈ Cloc(R,R) the inequalities |lik(u)(t)| ≤ lik(|u|)(t) (i, k = 1, . . . , n) (1.2) are fulfilled almost everywhere on R. A simple but important particular case of (1.1) is the linear differential system with deviated arguments xi(t) = n ∑ k=1 pik(t)xk(τik(t)) + qi(t) (i = 1, . . . , n), (1.3) 1991 Mathematics Subject Classification. 34K10.
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تاریخ انتشار 2002