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 | References | Similar Articles | Additional Information
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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Additional Information
Keywords:
Second order nonlinear oscillation,
boundedness,
linear oscillation
Article copyright:
© Copyright 1970
American Mathematical Society