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Proceedings of the American Mathematical Society

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

 

 

Nonlinear oscillation of a sublinear delay equation of arbitrary order


Authors: Takaŝi Kusano and Hiroshi Onose
Journal: Proc. Amer. Math. Soc. 40 (1973), 219-224
MSC: Primary 34K15
DOI: https://doi.org/10.1090/S0002-9939-1973-0324177-5
MathSciNet review: 0324177
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Abstract: The equations considered generalize

$\displaystyle {x^{(n)}}(t) + p(t)\vert x(g(t)){\vert^\alpha }\operatorname{sgn} x(g(t)) = 0,\quad 0 < \alpha < 1.$

A necessary and sufficient condition is established that all solutions are oscillatory when $ n$ is even and are either oscillatory or strongly monotone when $ n$ is odd. The result makes clear a difference in oscillatory property between sublinear delay equations and the corresponding ordinary differential equations.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0324177-5
Keywords: Oscillatory, nonoscillatory, sublinear, nonlinear delay equation
Article copyright: © Copyright 1973 American Mathematical Society