## Regularly varying solutions of perturbed Euler differential equations and related functional differential equations.(English)Zbl 1299.34174

Summary: An asymptotic analysis in the framework of Karamata regularly varying functions is performed for the solutions of second-order linear differential and functional differential equations in the critical case i.e., when the condition $$\lim_{t\to\infty}t\int_t^\infty q(s)\,ds=\frac14$$ holds.

### MSC:

 34D05 Asymptotic properties of solutions to ordinary differential equations 34C11 Growth and boundedness of solutions to ordinary differential equations 34A30 Linear ordinary differential equations and systems 34K06 Linear functional-differential equations

Karamata
Full Text: