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The differential equation x" + a(t)f(x) = 0, t > 0, is considered under the condition that lim,.x fl'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 cl + c2t.

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