ON ASYMPTOTIC BEHAVIOUR OF SOLUTION OF NONLINEAR FUNCTIONAL DIFFERENTIAL EQUATION
by
Roman Koplatadze
Department of Mathematics, I. Javakhishvili Tbilisi State University,

Consider an operator differential equation of the form

u(n)(t)+F(u)(t)=0,

(1)

where n ≥ 2, F:C(R₊;R)→ L_loc(R₊;R) is continuous mappings. We study oscillatory properties of solutions of Eq. (1) when satisfying the condition F(u)(t) u(t) ≥ 0   for    t ≥ t₀   and    u(t) ≠ 0 or the conditionF(u)(t) u(t) ≤ 0   for    t ≥ t₀   and    u(t) ≠ 0.

Date received: January 22, 2010