About: Asymptotic behavior of increasing solutions to a system of n nonlinear differential equations

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We consider system a system of n nonlinear differential equations of Emden-Fowler type. We analyze the asymptotic behavior of the solutions to this system whose components are eventually positive increasing. In particular, we derive exact asymptotic formulas for the extreme case, where all the solution components tend to infinity (the so-called strongly increasing solutions). We offer two approaches: one is based on the asymptotic equivalence theorem, and the other utilizes the theory of regular variation. The above-mentioned system includes, as special cases, two-term nonlinear scalar differential equations of arbitrary order n and systems of n/2 second-order nonlinear equations (provided n is even), which are related to elliptic partial differential systems. Applications to these objects are presented and a comparison with existing results is made. It turns out that some of our results yield new information even in the simplest case, a second-order Emden–Fowler differential equation. We consider system a system of n nonlinear differential equations of Emden-Fowler type. We analyze the asymptotic behavior of the solutions to this system whose components are eventually positive increasing. In particular, we derive exact asymptotic formulas for the extreme case, where all the solution components tend to infinity (the so-called strongly increasing solutions). We offer two approaches: one is based on the asymptotic equivalence theorem, and the other utilizes the theory of regular variation. The above-mentioned system includes, as special cases, two-term nonlinear scalar differential equations of arbitrary order n and systems of n/2 second-order nonlinear equations (provided n is even), which are related to elliptic partial differential systems. Applications to these objects are presented and a comparison with existing results is made. It turns out that some of our results yield new information even in the simplest case, a second-order Emden–Fowler differential equation. (en)
Title	Asymptotic behavior of increasing solutions to a system of n nonlinear differential equations Asymptotic behavior of increasing solutions to a system of n nonlinear differential equations (en)
skos:prefLabel	Asymptotic behavior of increasing solutions to a system of n nonlinear differential equations Asymptotic behavior of increasing solutions to a system of n nonlinear differential equations (en)
skos:notation	RIV/00216224:14410/13:00065974!RIV14-GA0-14410___
http://linked.open...avai/predkladatel	Pedagogická fakulta
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GAP201/10/1032)
http://linked.open...iv/cisloPeriodika	January
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Řehák, Pavel
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Masarykova univerzita / Pedagogická fakulta
http://linked.open...dnocenehoVysledku	62399
http://linked.open...ai/riv/idVysledku	RIV/00216224:14410/13:00065974
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Increasing solution; Asymptotic formula; Quasilinear system; Emden–Fowler system; Elliptic system; Regular variation (en)
http://linked.open.../riv/klicoveSlovo	Quasilinear system Elliptic system Emden–Fowler system Increasing solution Regular variation Asymptotic formula
http://linked.open...odStatuVydavatele	NL - Nizozemsko
http://linked.open...ontrolniKodProRIV	[D39087D932F9]
http://linked.open...i/riv/nazevZdroje	Nonlinear Analysis, Theory, Methods & Applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Difference equations and dynamic equations on time scales III
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	77
http://linked.open...iv/tvurceVysledku	Řehák, Pavel
http://linked.open...ain/vavai/riv/wos	000310502900003
issn	0362-546X
number of pages	14 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.na.2012.08.019
http://localhost/t...ganizacniJednotka	14410

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