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.

MSC:

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

Keywords:

Borel exceptional value
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References:

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