Principal pairs for oscillatory second order linear differential equations

Abstract

Nonoscillatory second order differential equations always admit ``special'', principal solutions. For a certain type of oscillatory equation principal pairs of solutions were introduced by \'A. Elbert, F. Neuman and J. Vosmansk\'y, {\em Diff. Int. Equations} {\bf 5} (1992), 945--960. In this paper, the notion of principal pair is extended to a wider class of oscillatory equations. Also an interesting property of some of the principal pairs is presented that makes the notion of these ``special'' pairs more understandable.