Nonoscillation theorems for a nonlinear differential equation

Gollwitzer, H. E.

doi:10.1090/S0002-9939-1970-0259243-3

Nonoscillation theorems for a nonlinear differential equation

Author: H. E. Gollwitzer
Journal: Proc. Amer. Math. Soc. 26 (1970), 78-84
MSC: Primary 34.42
DOI: https://doi.org/10.1090/S0002-9939-1970-0259243-3
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 $y'' + q(t)|y{|^\alpha }\operatorname {sgn} y = 0,\alpha > 0$, 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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