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A note on the zeros of solutions of $$w''+P(z)w=0$$, where P is a polynomial. (English) Zbl 0589.34008
For the class of equations described in the title, there is a classical result which states that there are (deg P)$$+2$$ critical rays, arg z$$=\theta_ j$$, such that for any $$\epsilon >0$$, all but finitely many zeros of any solution f(z)$$\not\equiv 0$$ must lie in the union of the sectors $$| \arg z-\theta_ j| <\epsilon$$. We prove that any infinite set of zeros in such a sector (for sufficiently small $$\epsilon)$$ must actually approach a definite ray, which is a translate of the critical ray (and which can be explicitly calculated). In addition, we estimate the rate at which the zeros approach the ray.

##### MSC:
 34M99 Ordinary differential equations in the complex domain 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
##### Keywords:
second order differential equation; critical rays
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##### References:
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