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

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.