R. Koplatadze

A. Razmadze Mathematical Institute, Georgian Academy of Sciences Tbilisi, Georgia

COMPARISON THEOREMS FOR DEVIATED DIFFERENTIAL EQUATIONS

Consider the equations

u^{(n)}(t) + ∑_{i=1}^{m} p_{i}(t)u(τ_{i}(t)) = 0,  (1)

v^{(n)}(t) + ∑_{i=1}^{k} q_{i}(t)v(σ_{i}(t)) = 0,  (2)

where m, k ∈ N, n ≥ 2, p_{i} ∈ L_{loc}(R_{+}; R) (i = 1, …, m), q_{i} ∈ L_{loc}(R_{+}; R)

(i = 1, …, k), τ_{i} ∈ C(R_{+}; R_{+}), lim_{t→+∞} τ_{i}(t) = +∞ (i = 1, …, m), σ_{i} ∈

C(R_{+}; R_{+}), lim_{t→+∞} σ_{i}(t) = +∞ (i = 1, …, k). Comparison theorems of new

type are established for the equations (1), (2) which enable one to obtain sufficient conditions for the equations (1) to have properties A and B.