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

Naito, Manabu

doi:10.1090/S0002-9947-1984-0732107-9

Asymptotic behavior of solutions of second order differential equations with integrable coefficients
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by Manabu Naito PDF

Trans. Amer. Math. Soc. 282 (1984), 577-588 Request permission

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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