A necessary and sufficient condition for oscillation of the Sturm–Liouville dynamic equation on time scales

In this paper, we investigate oscillatory properties of the second order Sturm–Liouville dynamic equation on a time scale (∗) (r(t)x Δ ) Δ +c(t)x σ=0. Using the so-called trigonometric transformation we establish a necessary and sufficient condition for oscillation of (∗). This condition is then use...

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Bibliographic Details
Published in:	Journal of computational and applied mathematics Vol. 141; no. 1; pp. 147 - 158
Main Authors:	Došlý, Ondřej, Hilger, Stefan
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01-04-2002
Subjects:	Measure chain Sturm–Liouville dynamic equations Symplectic dynamic systems Time scales Trigonometric transformation Measure chain Trigonometric transformation 39 A 10 Sturm–Liouville dynamic equations Symplectic dynamic systems Time scales
Online Access:	Get full text
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Summary:	In this paper, we investigate oscillatory properties of the second order Sturm–Liouville dynamic equation on a time scale (∗) (r(t)x Δ ) Δ +c(t)x σ=0. Using the so-called trigonometric transformation we establish a necessary and sufficient condition for oscillation of (∗). This condition is then used to derive an explicit oscillation criterion for this equation.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0377-0427 1879-1778
DOI:	10.1016/S0377-0427(01)00442-3