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On the distribution of zeros of solutions of second order differential equations. (Chinese. English summary) Zbl 1199.34475

Summary: We investigate the distribution of zeros of solutions of the second order differential equation \[ f''+A(z)f= 0, \] where \(A(z)\) is an entire function of finite order. By using Nevanlinna’s characteristic function and Ahlfors-Shimizu’s characteristic function, on an angular domain, we establish the existence of some ray with the property that, in its neighborhood, the exponent of convergence of the zero-sequence is infinite.

MSC:

34M10 Oscillation, growth of solutions to ordinary differential equations in the complex domain
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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