Existence of eventually positive solutions of fourth order quasilinear differential equations

We consider the fourth order quasilinear differential equation ( p ( t ) | u ″ | α − 1 u ″ ) ″ + q ( t ) | u | β − 1 u = 0 , where α and β are positive constants, p , q ∈ C [ a , ∞ ) , a > 0 , and p ( t ) > 0 , q ( t ) > 0 for t ⩾ a , and establish necessary and sufficient integral conditions for the existence of eventually positive solutions of the fourth order quasilinear differential equations.