an:06319197
Zbl 1299.34284
Latreuch, Zinela??bidine; Bela??di, Benharrat; El Farissi, Abdallah
Complex oscillation of differential polynomials in the unit disc
EN
Period. Math. Hung. 66, No. 1, 45-60 (2013).
00325838
2013
j
34M10 30D35 34M03
linear differential equations; analytic function; hyper-order; exponent of convergence of the sequence of distinct zeros
Summary: We consider the complex differential equations
\[
f''+A_1(z)f'+A_0(z)f = F,
\]
where \(A_0\not\equiv 0\), \(A_1\) and \(F\) are analytic functions in the unit disc \(\Delta =\{z : | z| < 1\}\). We obtain results on the order and the exponent of convergence of zero-points in \(\Delta\) of the differential polynomials \(g_f = d_2 f'' + d_1 f' +d_ 0f\) with non-simultaneously vanishing analytic coefficients \(d_2\), \(d_1\), \(d_0\). We answer a question posed by \textit{J. Tu} and \textit{C. F. Yi} [J. Math. Anal. Appl. 340, No. 1, 487--497 (2008; Zbl 1141.34054)] for the case of second-order linear differential equations in the unit disc.
Zbl 1141.34054