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Proceedings of the American Mathematical Society

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



Nonoscillation theorems for a nonlinear differential equation

Author: H. E. Gollwitzer
Journal: Proc. Amer. Math. Soc. 26 (1970), 78-84
MSC: Primary 34.42
MathSciNet review: 0259243
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Abstract: This paper is concerned with the problem of specifying growth conditions on the positive function $ q(t)$ which imply that all solutions of the nonlinear second order ordinary differential equation $ y'' + q(t)\vert y{\vert^\alpha }\operatorname{sgn} y = 0,\alpha > 0$, are nonoscillatory on a half line. Several different results are given, and the usual explicit monotonicity condition on $ q$ has been avoided to a certain degree.

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Keywords: Nonoscillation, nonlinear, second order, bounded variation, Riemann-Stieltjes integral
Article copyright: © Copyright 1970 American Mathematical Society