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Proceedings of the American Mathematical Society

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Monotone and oscillatory solution of $ y\sp{(n)}+py=0$


Author: W. J. Kim
Journal: Proc. Amer. Math. Soc. 62 (1977), 77-82
MSC: Primary 34C10
MathSciNet review: 0425256
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Abstract: Monotone and oscillatory behaviors of the solutions with the property that $ y(x)/{x^2} \to 0$ as $ x \to \infty $ or $ y(x)/x \to 0$ as $ x \to \infty $ are discussed. For example, it is shown that every nonoscillatory solution y, such that $ y(x)/x \to 0$ as $ x \to \infty $, monotonically tends to zero as $ x \to \infty $, provided n is odd, $ p \geqq 0$, and $ {\smallint ^\infty }{x^{n - 1}}p(x)dx = \infty $.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0425256-8
Keywords: Monotone and oscillatory solutions, asymptotic behavior, linear equations, ordinary, nth-order, real-valued continuous coefficients
Article copyright: © Copyright 1977 American Mathematical Society