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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

Keywords:

Karamata
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