About: Bounded solutions and wavefronts for discrete dynamics

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	This paper deals with the second order nonlinear difference equation $$ \dd(r_k\dd u_k)+q_kg(u_{k+1})=0, $$ where $ \{r_k\} $ and $ \{q_k\} $ are positive real sequences defined on $\N\cup \{0\}$, and the nonlinearity $g:\R \to \R $ is nonnegative and nontrivial. Sufficient and necessary conditions are given, for the existence of bounded solutions starting from a fixed initial condition $u_0$. The same dynamic, with $f$ instead of $g$ such that $uf(u)>0$ for $u\not=0$, was recently extensively investigated. On the contrary, our nonlinearity $ g $ is of a small appearance in the discrete case. Its introduction is motivated by the analysis of wavefront profiles in biological and chemical models. The paper emphasizes the many different dynamical behaviors caused by such a $g$ with respect to the equation involving function $f$. Some applications in the study of wavefronts complete this work. This paper deals with the second order nonlinear difference equation $$ \dd(r_k\dd u_k)+q_kg(u_{k+1})=0, $$ where $ \{r_k\} $ and $ \{q_k\} $ are positive real sequences defined on $\N\cup \{0\}$, and the nonlinearity $g:\R \to \R $ is nonnegative and nontrivial. Sufficient and necessary conditions are given, for the existence of bounded solutions starting from a fixed initial condition $u_0$. The same dynamic, with $f$ instead of $g$ such that $uf(u)>0$ for $u\not=0$, was recently extensively investigated. On the contrary, our nonlinearity $ g $ is of a small appearance in the discrete case. Its introduction is motivated by the analysis of wavefront profiles in biological and chemical models. The paper emphasizes the many different dynamical behaviors caused by such a $g$ with respect to the equation involving function $f$. Some applications in the study of wavefronts complete this work. (en) Je studována nelineární diferenční rovnice. Jsou odvozeny postačující a nutné podmínky pro existenci ohraničných řešení startujících v daném bodě. (cs)
Title	Bounded solutions and wavefronts for discrete dynamics Ohraničená řešení a vlnoplochy v diskrétní dynamice (cs) Bounded solutions and wavefronts for discrete dynamics (en)
skos:prefLabel	Bounded solutions and wavefronts for discrete dynamics Ohraničená řešení a vlnoplochy v diskrétní dynamice (cs) Bounded solutions and wavefronts for discrete dynamics (en)
skos:notation	RIV/00216224:14410/04:00011418!RIV08-GA0-14410___
http://linked.open.../vavai/riv/strany	1079-1094
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/01/0079), P(GP201/01/P041), Z(AV0Z1019905)
http://linked.open...iv/cisloPeriodika	6-7
http://linked.open...vai/riv/dodaniDat	2008
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	556506
http://linked.open...ai/riv/idVysledku	RIV/00216224:14410/04:00011418
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	nonlinear difference equation; bounded solution; nonnegative nonlinearity; discrete travelling wave solution (en)
http://linked.open.../riv/klicoveSlovo	nonlinear difference equation bounded solution discrete travelling wave solution nonnegative nonlinearity
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[B810A2B9F3D6]
http://linked.open...i/riv/nazevZdroje	Computers & mathematics with applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Qualitative theory of solutions of difference equations Qualitative theory of half-linear differential and difference equations
http://linked.open...UplatneniVysledku	2004
http://linked.open...v/svazekPeriodika	47
http://linked.open...iv/tvurceVysledku	Řehák, Pavel Malaguti, Luisa Taddei, Valentina
http://linked.open...n/vavai/riv/zamer	Complex development of all branches of mathematics with regard to the needs of physics and technology
issn	0097-4943
number of pages	26 (xsd:int)
http://localhost/t...ganizacniJednotka	14410

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