Proceedings of the American Mathematical Society

Author(s): James S. W. Wong
Journal: Proc. Amer. Math. Soc. 127 (1999), 1387-1395.
MSC (1991): Primary 34C10, 34C15
Posted: January 28, 1999
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 34C10, 34C15

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

DOI: 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
Posted: January 28, 1999
Communicated by: Hal L. Smith
Copyright of article: Copyright 1999, American Mathematical Society

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