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Perturbative Oscillation Criteria and Hardy-Type Ineqalities

✍ Scribed by F. Gesztesy; M. Ünal

Book ID
102941584
Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
855 KB
Volume
189
Category
Article
ISSN
0025-584X

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✦ Synopsis

We prove a natural generalization of Kneser's oscillation criterion and Hardy's inequality for Sturm -Liouville differential expressions. In particular, assuming -&po(x) & + qo(x), x E (a, b), -00 5 a < b 5 00, to be nonoscillatory near a (or b), we determine conditions on q(x) such that -&po(z)$ + qo(x) + q(z) is nonoscillatory, respectively, oscillatory near a (or b). q E Ltoc (( a, b)) is realvalued . 1991 Mathematics Subject Classification. Keywords and phrases. Sturm -Liouville operators.

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