Article contents
A classification of the solutions of a differential equation according to their asymptotic behaviour
Published online by Cambridge University Press: 14 November 2011
Synopsis
The solutions of the differential equation Lny + p(x)y = 0, where Lny = ρn(ρn−1 … (ρ1(ρ0y)′)′ …)′ and p(x) is of one sign, are classified according to their behaviour as x → ∞. The solution space is decomposed into disjoint, non-empty sets Sk, 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 sets Sk, the structure of the sets and its connection with (k, n − k)-disfocality.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 83 , Issue 1-2 , 1979 , pp. 25 - 38
- Copyright
- Copyright © Royal Society of Edinburgh 1979
References
- 9
- Cited by