On oscillation theorems for differential polynomials. (English) Zbl 1183.34135

El Farissi, A.; Belaidi, B.

Electron. J. Qual. Theory Differ. Equ. 2009, Paper No. 22, 10 p. (2009).

Summary: We investigate the relationship between small functions and differential polynomials \(g_{f}\left( z\right)=d_{2}f^{^{\prime \prime }} + d_{1}f^{^{\prime }}+d_{0}f\), where \(d_0, d_1, d_2\) are meromorphic functions that are not all equal to zero with finite order generated by solutions of the second order linear differential equation
\[ f''+Af'+Bf=F, \]
where \(A,B,F\not\equiv 0\) are finite order meromorphic functions having only finitely many poles.

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

Keywords:

linear differential equations; meromorphic solutions; order of growth; exponent of convergence of zeros; exponent of convergence of distinct zeros; differential polynomials