Unexpected behavior for solutions of a second order, selfadjoint equation

Abstract:

Positive, continuous functions $a(t)$ and $p(t)$ such that $a(t)p(t) \equiv t$ and for which some solution of the selfadjoint equation $(pu’)’ + au = 0$ satisfies $\lim \;{\sup _{t \to \infty }}|u(t)| > 0$ are shown to exist.