Structure of the solution space of certain linear equations (Q1089820)

This paper is concerned with even order differential equations of the form \(y^{(2n)}+P(x)y=0\) on \(I=[0,\infty)\), where P is a nonzero continuous function on I. The objective is to describe the structure of the solution space of this equation in terms of the oscillation or nonoscillation of certain types of solutions. In this context a solution \(y=y(x)\) is said to be oscillatory if it has infinitely many isolated zeros on I: otherwise it is described as nonoscillatory. There is also discussion of the cases in which \(P<0\) and \(P>0\) on I.