The Asymptotic Behavior Of Nonoscillatory Solutions Of A Class Of Third Order Quasilinear Differential Equations

This paper is concerned with nonoscillatory solutions of the third order quasilinear differential equationwhere α > 0, β > 0, p(t) and q(t) are continuous functions on an infinite interval [a, ∞) satisfying p(t) > 0 and q(t) > 0, t ≥ a. The growth bounds near t = ∞ of nonoscillatory solutions are obtained, and necessary and sufficient integral conditions are established for the existence of nonoscillatory solutions having specific asymptotic growths as t → ∞, when the equation satisfies dt = ∞ or dt < ∞.