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Proceedings of the American Mathematical Society

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

 

 

Nonoscillatory solutions of second order differential equations with integrable coefficients


Author: Manabu Naito
Journal: Proc. Amer. Math. Soc. 109 (1990), 769-774
MSC: Primary 34C10; Secondary 34C11
DOI: https://doi.org/10.1090/S0002-9939-1990-1019278-2
MathSciNet review: 1019278
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Abstract: The asymptotic behavior of nonoscillatory solutions of the equation $ x'' + a\left( t \right){\left\vert x \right\vert^\gamma }\operatorname{sgn} x = 0,\gamma > 0$, is discussed under the condition that $ A\left( t \right) = {\text{li}}{{\text{m}}_{T \to \infty }}\int_t^T {a\left( s \right)ds} $ exists and $ A\left( t \right) \geq 0$ for all $ t$. For the sublinear case of $ 0 < \gamma < 1$, the existence of at least one nonoscillatory solution is completely characterized.


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DOI: https://doi.org/10.1090/S0002-9939-1990-1019278-2
Article copyright: © Copyright 1990 American Mathematical Society