| MALAGUTI, Luisa, Pavel ŘEHÁK and Valentina TADDEI. Bounded solutions and wavefronts for discrete dynamics. Computers & Mathematics with Applications. New York: Pergamon Press, 2004, vol. 47, 6-7, p. 1079-1094, 26 pp. ISSN 0898-1221. |
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@article{554400,
author = {Malaguti, Luisa and Řehák, Pavel and Taddei, Valentina},
article_location = {New York},
article_number = {6-7},
keywords = {nonlinear difference equation; bounded solution; nonnegative nonlinearity; discrete travelling wave solution},
language = {eng},
issn = {0898-1221},
journal = {Computers & Mathematics with Applications},
title = {Bounded solutions and wavefronts for discrete dynamics},
volume = {47},
year = {2004}
}
TY - JOUR
ID - 554400
AU - Malaguti, Luisa - Řehák, Pavel - Taddei, Valentina
PY - 2004
TI - Bounded solutions and wavefronts for discrete dynamics
JF - Computers & Mathematics with Applications
VL - 47
IS - 6-7
SP - 1079-1094
EP - 1079-1094
PB - Pergamon Press
SN - 08981221
KW - nonlinear difference equation
KW - bounded solution
KW - nonnegative nonlinearity
KW - discrete travelling wave solution
N2 - 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.
ER -
MALAGUTI, Luisa, Pavel ŘEHÁK and Valentina TADDEI. Bounded solutions and wavefronts for discrete dynamics. \textit{Computers \&{} Mathematics with Applications}. New York: Pergamon Press, 2004, vol.~47, 6-7, p.~1079-1094, 26 pp. ISSN~0898-1221.
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