A trichotomy of solutions of second order linear differential equations. (English) Zbl 0597.34060

Summary: The main result of this paper is contained in the lemma, in which a sufficient condition is given such that all positive decreasing solutions of equation \(y''=f(x)y\) are slowly or rapidly or regularly varying functions. By using the lemma some inequalities for the solution of the above equation are obtained.


34E05 Asymptotic expansions of solutions to ordinary differential equations
34A30 Linear ordinary differential equations and systems