A classification of the solutions of a differential equation according to their asymptotic behaviour
Uri Elias · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1979
Synopsis The solutions of the differential equationLny+p(x)y= 0, whereLny= ρn(ρn−1… (ρ1(ρ0y)′)′ …)′ andp(x) is of one sign, are classified according to their behaviour asx→ ∞. The solution space is decomposed into disjoint, non-empty setsSk, 0≦K≦n, such that (−1)n−kp(x)≦0. We study the growth properties and the density of the zeros of the solutions which belong to the different setsSk, the structure of the sets and its connection with (k,n−k)-disfocality.