The growth and Borel direction of solutions of a class of linear differential equations. (Chinese. English summary) Zbl 1438.34337
Summary: In this paper, we mainly use the value distribution theory to study the oscillation of solutions of linear differential equations \[f'' + Af' + Bf = 0,\] where \(A\), \(B\) are entire functions. With some added conditions on coefficients, we find that every solution \(f \ne 0\) of the equation has infinite order and at least two Borel directions in a certain angular.
MSC:
| 34M03 | Linear ordinary differential equations and systems in the complex domain |
| 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 |
