Nonoscillatory solutions of second order differential equations with integrable coefficients
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- by Manabu Naito PDF
- Proc. Amer. Math. Soc. 109 (1990), 769-774 Request permission
Abstract:
The asymptotic behavior of nonoscillatory solutions of the equation $x'' + a\left ( t \right ){\left | x \right |^\gamma }\operatorname {sgn} x = 0,\gamma > 0$, 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.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- 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