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On Small Random Perturbations of a Second-Order Differential Equation

✍ Scribed by Dubrovskii, V. N.

Book ID
118227776
Publisher
Society for Industrial and Applied Mathematics
Year
1974
Tongue
English
Weight
870 KB
Volume
18
Category
Article
ISSN
0040-585X

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## Abstract We give constructive proof of the existence of vanishing at infinity oscillatory solutions for a second‐order perturbed nonlinear differential equation. In contrast to most results reported in the literature, we do not require oscillatory character of the associated unperturbed equation

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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