## Finite order solutions of second order linear differential equations.(English)Zbl 0634.34004

Summary: We consider the differential equation $$f''+A(z)f'+B(z)f=0$$ where A(z) and B(z) are entire functions. We will find conditions on A(z) and B(z) which will guarantee that every solution $$f\not\equiv 0$$ of the equation will have infinite order. We will also find conditions on A(z) and B(z) which will guarantee that any finite order solution $$f\not\equiv 0$$ of the equation will not have zero as a Borel exceptional value. We will also show that if A(z) and B(z) satisfy certain growth conditions, then any finite order solution of the equation will satisfy certan other growth conditions. Related results are also proven. Several examples are given to complement the theory.

### MSC:

 34M99 Ordinary differential equations in the complex domain 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory 34C11 Growth and boundedness of solutions to ordinary differential equations 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34A30 Linear ordinary differential equations and systems

### Keywords:

second order differential quation; examples
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### References:

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