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On the number of zeros of bounded nonoscillatory solutions to higher-order nonlinear ordinary differential equations

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*
Manabu Naito
*

** Address.**
Department of Mathematics, Faculty of Science, Ehime University, Matsuyama 790-8577, Japan

** E-mail:**
mnaito@math.sci.ehime-u.ac.jp

**Abstract.**
The higher-order nonlinear ordinary differential equation
$$
x^{(n)} + \lambda p(t)f(x) = 0\,, \quad t \geq a\,,
$$
is considered and the problem of counting the number of zeros of bounded
nonoscillatory solutions $x(t;\lambda)$ satisfying $\lim_{t\to\infty}x(t;\lambda) =
1$ is studied. The results can be applied to a singular eigenvalue problem.

**AMSclassification. ** 34C10, 34B40, 34B15.

**Keywords. **Nonoscillatory solutions, zeros of solutions, singular eigenvalue problems.