Geodesic
On the number of zeros of bounded nonoscillatory solutions to higher-order nonlinear ordinary differential equations
Archivum mathematicum, Tome 43 (2007) no. 1, pp. 39-53

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The higher-order nonlinear ordinary differential equation \[ x^{(n)} + \lambda p(t)f(x) = 0\,, \quad t \ge a\,, \] is considered and the problem of counting the number of zeros of bounded nonoscillatory solutions $x(t;\lambda )$ satisfying $\lim _{t\rightarrow \infty }x(t;\lambda ) = 1$ is studied. The results can be applied to a singular eigenvalue problem.
Classification : 34B40, 34C10
Keywords: nonoscillatory solutions; zeros of solutions; singular eigenvalue problems 
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     title = {On the number of zeros of bounded nonoscillatory solutions to higher-order nonlinear ordinary differential equations},
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Naito, Manabu. On the number of zeros of bounded nonoscillatory solutions to higher-order nonlinear ordinary differential equations. Archivum mathematicum, Tome 43 (2007) no. 1, pp. 39-53. http://geodesic.mathdoc.fr/item/ARM_2007__43_1_a3/