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Zbl 0681.33008
Laforgia, Andrea; Muldoon, Martin E.
Monotonicity properties of zeros of generalized Airy functions. (English)
[J] Z. Angew. Math. Phys. 39, No.2, 267-271 (1988). ISSN 0044-2275; ISSN 1420-9039/e

The generalized Airy function is a solution of the differential equation $$ (1)\quad y''+x\sp{\alpha}y=0,\quad x\in [0,\infty), $$ where $\alpha$ is a positive number. From the introduction: ``M. S. P. Eastham conjectured that the first positive zero $a\sb{\alpha 1}$ of a solution of (1) with $y(0)=0$, decreases as $\alpha$ increases. We show here that this decrease (to 1) occurs for all positive zeros of such a solution and indeed for all, except possibly the first of the zeros of any nontrivial solution of (1) even without the condition $y(0)=0.$''
[L.Littlejohn]

MSC 2000:: *33C10 Cylinder functions, etc.
34C10 Qualitative theory of oscillations of ODE: Zeros, etc.
34B30 Special ODE

Keywords: monotonicity of zeros; Airy function

Cited in: Zbl 0731.33002

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