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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Oscillation theorems for second order nonlinear differential equations.


Author: Lynn Erbe
Journal: Proc. Amer. Math. Soc. 24 (1970), 811-814
MSC: Primary 34.42
DOI: https://doi.org/10.1090/S0002-9939-1970-0252756-X
MathSciNet review: 0252756
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Abstract: The oscillatory and nonoscillatory behavior of the nonlinear second order differential equation $ (1)\;x'' + p(t)f(x) = 0$ is related to that of $ {(2)_\lambda }\;x'' + \lambda p(t)x = 0,\;\lambda > 0$. Under certain conditions on $ p(t)$ and $ f(x)$ it is shown that all solutions of $ (1)$ are oscillatory if $ {(2)_\lambda }$ is oscillatory for all $ \lambda > 0$. In contrast to most of the literature on this subject, no sign or integrability conditions on $ p(t)$ are explicitly assumed.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0252756-X
Keywords: Second order nonlinear oscillation, boundedness, linear oscillation
Article copyright: © Copyright 1970 American Mathematical Society