On the existence of eventually positive solutions of fourth-order quasilinear differential equations Original Research Article

The fourth-order quasilinear differential equation equation(1.1) (|u″|α−1u″)″+q(t)|u|β−1u=0 is considered under the assumptions that α>0, β>0 and q(t) is a positive continuous function on an interval [a,∞), a>0, and the necessary and sufficient integral conditions for the existence of eventually positive solutions of (1.1) are established.