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Oscillatory Properties of Second Order Half-Linear Difference Equations

✍ Scribed by Pavel Rehak


Book ID
110324178
Publisher
Springer
Year
2001
Tongue
English
Weight
183 KB
Volume
51
Category
Article
ISSN
0011-4642

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πŸ“œ SIMILAR VOLUMES


Nonoscillation criteria for half-linear
✍ O. DoΕ‘lΓ½; P. ŘehΓ‘k πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 462 KB

Nonoscillation criteria for the half-linear second-order difference equation ZX(rkΒ’,(~Xxk))+ck~(Xk+l) =0, ~,(x) := IxlP-2x, p> 1, are established. These criteria are derived using the Riccati and variational technique.

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The authors consider second-order difference equations of the type A ((~~~)") + w&,, = 0, (E) where cz 10 is the ratio of odd positive integers, {qn} is a positive sequence, and {u(n)} is a positive increasing sequence of integers with o(n) -+ co as n + cc. They give some oscillation and comparison

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In this paper, we obtain new sufficient conditions for the oscillation of all solutions of the second-order linear difference equation where Axn = xt,+1 --xn is the forward difference operator, {Ph} is a sequence of nonnegative real numbers. Our results improve the know results in the literature.