Conjugacy and phases for second order linear difference equation
✍ Scribed by Zuzana Došlá; Šárka Pechancová
- Book ID
- 108077062
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 254 KB
- Volume
- 53
- Category
- Article
- ISSN
- 0898-1221
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📜 SIMILAR VOLUMES
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
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.
Nonoscillation criteria for the half-linear second-order difference equation ZX(rk¢,(~Xxk))+ck~(Xk+l) =0, ~,(x) := IxlP-2x, p> 1, are established. These criteria are derived using the Riccati and variational technique.