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The higher-order nonlinear ordinary differential equation
is considered and the problem of counting the number of zeros of bounded nonoscillatory solutions satisfying is studied. The results can be applied to a singular eigenvalue problem.
In this paper we have considered completely the equation
where , , and such that , and . It has been shown that the set of all oscillatory solutions of (*) forms a two-dimensional subspace of the solution space of (*) provided that (*) has an oscillatory solution. This answers a question raised by S. Ahmad and A. C. Lazer earlier.
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