On the oscillation of solutions of certain linear differential equations in the complex domain. (English) Zbl 0596.30049

Let A(z) be an entire function of finite order having zero as a Borel exceptional value. Conditions are given on the location of zeros of A(z) which ensure that all non-trivial solutions of \[ y^{(k)}+(A(z)+Q(z))y=0, \] where \(k\geq 2\) and Q is a sufficiently small polynomial, have zeros with infinite exponent of convergence. In particular this is true for all solutions of \(y^{(k)}+e^{P(z)}y=0,\) if \(k\geq 2\) and P is a non-constant polynomial.


30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
34M99 Ordinary differential equations in the complex domain
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