Asymptotic problems for functional differential equations via linearization method

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Authors	DOŠLÁ Zuzana LIŠKA Petr MARINI Mauro
Year of publication	2019
Type	Article in Periodical
Magazine / Source	JOURNAL OF FIXED POINT THEORY AND APPLICATIONS
MU Faculty or unit	Faculty of Science
Citation
Web	https://link.springer.com/article/10.1007/s11784-018-0642-2
Doi	http://dx.doi.org/10.1007/s11784-018-0642-2
Keywords	Second order nonlinear differential equation; Kneser solution; zero-decaying solution; super-linear equation; sub-linear equation
Description	We study the existence of positive decreasing solutions (the so-called Kneser solutions) for a class of second-order functional differential equations with a damping term. A linearization approach based on a general fixed point theorem is used to achieve this goal. The existence of zero-decaying Kneser solutions is also proved. Finally, the role of the deviating argument to the asymptotic behavior of solutions is illustrated together with some discrepancies between equations with or without delay.
Related projects:	Asymptotická teorie obyčejných diferenciálních rovnic celočíselných a neceločíselných řádů a jejich numerických diskretizací