On The Existence Of Eventually Positive Solutions Of Forth-order Quasilinear Differential Equations

This paper is concerned with nonoscillatory solution of the fourth order quasilinear differential equationwhereα＞0,β＞0, p(t), q(t) are positive continuous functions on a finite interval [α,∞) The necessary and sufficient integral condition for the existence of eventually positive solutions of the equation above are established by Wu when the equation satisfiesα≤1＜βorα≥1＞β. In fact, we can proved a stronger result which required a weaker condition onαandβ, namelyα＜β. In this paper, we obtain an necessary and sufficient integral conditions for the existence of eventually positive solution of the equation above, which is more general.