𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the Nonoscillatory Behavior of Solutions of a Second Order Linear Differential Equation

✍ Scribed by Horng-Jaan Li; Cheh-Chih Yeh

Publisher
John Wiley and Sons
Year
1996
Tongue
English
Weight
633 KB
Volume
182
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, we improve the Sturm comparison theorem and two nonoscillation criteria of LEIGHTON and WINTNER, and establish two variants of a WINTNER'S nonoscillatory criterion of the second order linear differential equation

where r, c : [to,co) -+ IR, T > 0 a.e. on [to,m) and f , c E L 1 ( t o , b ) for each b E (to,m) for some to 2 0. Using these two criteria, we improve some nonoscillation criteria of HARTMAN. HILLE. MOORE, POTTER. WINTNER, and WILLETT. These proofs are more elegant and concise than those of theirs.

  • F ( t ) } ,

πŸ“œ SIMILAR VOLUMES

Linear Perturbations of a Nonoscillatory
Linear Perturbations of a Nonoscillatory Second Order Difference Equation
✍ William F. Trench πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 86 KB

Let x 1n and x 2n be recessive and dominant solutions of the nonoscillatory difference equation r n-1 x n-1 + p n x n = 0. It is shown that if ∞ f n x 1n x 2n converges (perhaps conditionally) and satisfies a second condition on its order of covergence, then the difference equation r n-1 y n-1 + p n