On Petrenko's deviations and second order differential equations

2020/01/17 by J. Heittokangas, Janne Heittokangas, Heittokangas, J. +3
Mathematics · #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics #Meromorphic and Entire Functions #Primary 34M10 #Secondary 30D35 #math.CV #msc:30D35 #msc:34M10

paper · pdf · doi:10.48550/arxiv.2001.06250

9 pages

arxiv created 2020/01/17 · openalex publication_date 2020/01/17 · arxiv updated 2020/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

New results on the oscillation of solutions of f''+A(z)f=0 and on the growth of solutions of f''+A(z)f'+B(z)f=0 are obtained, where A and B are entire functions. Petrenko's magnitudes of deviation of g with respect to ∞ play a key rôle in the results, where g represents one of the coefficients A or B. These quantities are defined by β^-(∞,g) = \liminf_r→∞ (log M(r,g))/(T(r,g)) and β⁺(∞,g) = \limsup_r→∞ (log M(r,g))/(T(r,g)).

Citations

• On Integral Functions Having Prescribed Asymptotic Growth

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