On the Relation Between Boundedness and Oscillation of Differential Equations of Second Order

Abstract

In this paper we are dealing with differential equations of the forms:Eiwhere the functions pi are positive.By a solution of an equation of the above forms, we mean a function x(t) ∈ C2 [c, + ∞) where c is a non-negative constant, which satisfies the corresponding equation on the whole interval [c, +∞). By an oscillatory solution of (Ei), we mean a solution with arbitrarily large zeros.