Gil’, Michael Inequalities for zeros of solutions to second order ODE with one singular point. (English) Zbl 1335.34140 Differ. Equ. Appl. 8, No. 1, 69-76 (2016). Summary: We consider the equation \[ y''+ P(z)y'+ Q(z)y= 0\;(z\in\mathbb{C}), \] where \[ P(z)= \sum^{n_P}_{k=0} p_kz^{k-1}\quad\text{and}\quad Q(z)= \sum^{n_Q}_{k=0} q_k z^{k-2} \] with real coefficients \(p_k\), \(q_j\) (\(k=0,, n_P\); \(j=0,\dots, n_Q\); \(n_P,n_Q<\infty\)). Let \(z_k(y)\), \(k= 1,2,\dots\) be the nontrivial zeros of a solution \(y(z)\) to that equation. Estimates for the sums \[ \sum^j_{k=1} {1\over |z_k(y)|}\;(j= 1,2,\dots) \] are derived. Applications of the obtained estimates to the counting function of the zeros of solutions are also discussed. Cited in 3 Documents 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 Keywords:ODE with a singular point; complex zeros of solutions; counting function; zero free domain PDFBibTeX XMLCite \textit{M. Gil'}, Differ. Equ. Appl. 8, No. 1, 69--76 (2016; Zbl 1335.34140) Full Text: DOI Link