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- W1996263744 abstract "with a small nonlinear term f(x, y). The exact conditions satisfied by r, q, and f will be given in ??2 and 3. If r, q, and (rq)' are real-valued continuous functions on the positive x-axis, in a recent paper [1 ] Walter Leighton proved that the following conditions rq>O and (rq)' >0 for x_?0 are sufficient for the boundedness of the solutions of the linear differential equation (ry')'+qy = 0 on the positive x-axis. It is the purpose of this note to point out that, even if rq is not differentiable (in fact, even the continuity of rq is not required), under certain suitable conditions satisfied by r, q, and f as stated in Theorems 1 and 2, we still can test the boundedness of the solutions of (1) by a method which includes Leighton's method as a special case. In ?2 we assume that r, q, and f are real-valued functions; in ?3, complex-valued." @default.
- W1996263744 created "2016-06-24" @default.
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- W1996263744 date "1954-01-01" @default.
- W1996263744 modified "2023-09-25" @default.
- W1996263744 title "The boundedness of the solutions of a nonlinear differential equation" @default.
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- W1996263744 doi "https://doi.org/10.1090/s0002-9939-1954-0061242-2" @default.
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