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Linear Perturbations of a Nonoscillatory Second Order Difference Equation

✍ Scribed by William F. Trench

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
86 KB
Volume
255
Category
Article
ISSN
0022-247X

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✦ Synopsis

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 y n = f n y n is also nonoscillatory and has recessive and dominant solutions y 1n and y 2n that behave asymptotically like x 1n and x 2n .

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