## 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.

### MSC:

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