Asymptotic behaviour of the maxima of solutions of certain differential equations (Q1291137)

The differential equation \(u''+qu=0\) is said to have the Wintner property if for all solutions the relative maxima of \(q^{1/4}| u |\) converge to a finite positive limit as \(t\to\infty\). Some new methods are described by which the Wintner property may be established in certain cases. On the other hand, the authors show that this property is exceptional: the set of \(q\) for which the equation has the Wintner property is residual in the sense of Baire category.