On Asymptotic Properties Of Solutions Of Third Order Linear Differential Equations With Deviating Arguments

. The asymptotic properties of solutions of the equation u 000 (t) = p 1 (t)u(ø 1 (t))+p 2 (t)u 0 (ø 2 (t)), are investigatedwhere p i : [a; +1[! R (i = 1; 2) are locally summable functions, ø i : [a; +1[! R (i = 1; 2) measurable ones and ø i (t) t (i = 1; 2). In particular, it is proved that if p 1 (t) 0, p 2 2 (t) ff(t)jp 1 (t)j, Z +1 a [ø 1 (t) \Gamma t] 2 p 1 (t)dt ! +1 and Z +1 a ff(t)dt ! +1; then each solution with the first derivative vanishing at infinity is of the Kneser type and a set of all such solutions forms a one-dimensional linear space. Let us consider the differential equation (1) u 000 (t) = p 1 (t)u(ø 1 (t)) + p 2 (t)u 0 (ø 2 (t)) ; where the functions p i : [a; +1[! R (i = 1; 2) are locally integrable and the functions ø i : [a; +1[!R (i = 1; 2) are measurable and (2) ø i (t) t for t a (i = 1; 2) : The solution u of the equation (1) will be called of the Kneser type if it satisfies the inequalities u 0 (t)u(t) 0; u 00 (t)u(t) 0 for ..