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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Nonoscillation theorems for second order
nonlinear differential equations


Author: James S. W. Wong
Journal: Proc. Amer. Math. Soc. 127 (1999), 1387-1395
MSC (1991): Primary 34C10, 34C15
Published electronically: January 28, 1999
MathSciNet review: 1622997
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Abstract: We prove nonoscillation theorems for the second order Emden-Fowler equation (E): $y''+a(x)|y|^{\gamma-1}y=0$, $\gamma>0$, where $a(x)\in C(0,\infty)$ and $\gamma\not=1$. It is shown that when $x^{(\gamma+3)/2+\delta}a(x)$ is nondecreasing for any $\delta>0$ and is bounded above, then (E) is nonoscillatory. This improves a well-known result of Belohorec in the sublinear case, i.e. when $0<\gamma<1$ and $0<\delta<(1-\gamma)/2$.


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Additional Information

James S. W. Wong
Affiliation: Chinney Investments Ltd., Hong Kong; City University of Hong Kong, Hong Kong

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05036-4
PII: S 0002-9939(99)05036-4
Keywords: Second order, nonlinear, ordinary differential equations, oscillation, asymptotic behavior
Received by editor(s): August 7, 1997
Published electronically: January 28, 1999
Communicated by: Hal L. Smith
Article copyright: © Copyright 1999 American Mathematical Society