On the frequency of zeros of solutions of second order linear differential equations. (English) Zbl 0635.34007

This paper continues work of the authors [Math. Zeitschr. 183, 355-364 (1983; Zbl 0494.34005); Trans. Am. Math. Soc. 273, 351-363 (1982; Zbl 0505.34026); Comment. Math. Helv. 58, 656-677 (1983; Zbl 0532.34008)] on the zeros of solutions of a differential equation in the complex plane, of the type \(f''+a(z)f=0\). The main result is that, under certain assumptions, for any two linearly independent solutions \(f_ 1(z)\) and \(f_ 2(z)\) we have \(\max (\lambda (f_ 1),\lambda (f_ 2))=+\infty,\) where \(\lambda\) (g) denotes the exponent of convergence of the zeros of g(z). The assumptions are that a(z) is a meromorphic function with some specified growth condition.
Reviewer: E.Roxin


34M99 Ordinary differential equations in the complex domain
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