The Asymptotic Behavior Of Nonoscillatory Solution Of Three-Dimensional Differential Systems

The three-dimensional differential systemis considered under the assumptions thatλ_i (i = 1, 2, 3) are positive constantsand a_i(t) (i = 1, 2, 3) are positive continuous functions on [0,∞),and the nessaryand sufficient integral conditions for the existence of eventually positive solutionof(S) having specific asymptotic growths as t→∞are established.The systemsatisfies∫₀^∞a_i(t) dt =∞, i = 1, 2.