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

Takaŝi, Kusano; Marić, Vojislav

Publ. Inst. Math., Nouv. Sér. 88(102), 1-20 (2010).

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