Stability criteria for second order linear ordinary differential equations

2019/05/16 by G. A. Grigorian, Grigorian, G. A.
Mathematics · Physics and Astronomy · #34C10 #34C11 #34C99 #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #F.2.2 #FOS: Mathematics #I.2.7 #Numerical methods for differential equations #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.1905.06552

openalex publication_date 2019/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use some properties of solutions of Riccati equation for establishing boundedness and stability criteria for solutions of second order linear ordinary differential equations. We show that the conditions on coefficients of the equations, appearing in the proven criteria, do not follow from the conditions, which ensure the application of the WKB approximation to the second order linear equations. On these examples we compare the obtained results wit the results obtained by the Liapunov and Bogdanov methods, by a method involving estimates of solutions in the Lozinski's logarithmic norms, and by the freezing method. We compare these results with the Wazevski's theorem as well.

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