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Asymptotic behavior of solutions of second order differential equations with integrable coefficients


Author: Manabu Naito
Journal: Trans. Amer. Math. Soc. 282 (1984), 577-588
MSC: Primary 34D05
DOI: https://doi.org/10.1090/S0002-9947-1984-0732107-9
MathSciNet review: 732107
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Abstract: The differential equation $ x'' + a(t)f(x) = 0$, $ t > 0$, is considered under the condition that $ {\lim_{t \to \infty }}{\int ^t}a(s)ds$ exists and is finite, and necessary and/or sufficient conditions are given for this equation to have solutions which behave asymptotically like nontrivial linear functions $ {c_1} + {c_2}t$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1984-0732107-9
Keywords: Asymptotic integration, asymptotic behavior, differential equations
Article copyright: © Copyright 1984 American Mathematical Society

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