zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On a generalized max-type difference equation from automatic control theory. (English) Zbl 1194.39007
The boundedness character of positive solutions of the difference equation of the form $$x_{n+1}=\max\left\{A,\frac{x_n^p}{x_{n-1}^qx_{n-2}^r}\right\},\quad n\in\Bbb N_0,$$ is studied.

MSC:
39A20Generalized difference equations
39A22Growth, boundedness, comparison of solutions (difference equations)
WorldCat.org
Full Text: DOI
References:
[1] Berenhaut, K.; Foley, J.; Stević, S.: Boundedness character of positive solutions of a MAX difference equation, J. difference equ. Appl. 12, No. 12, 1193-1199 (2006) · Zbl 1116.39001 · doi:10.1080/10236190600949766
[2] Berezansky, L.; Braverman, E.: On impulsive beverton--Holt difference equations and their applications, J. difference equ. Appl. 10, No. 9, 851-868 (2004) · Zbl 1068.39005 · doi:10.1080/10236190410001726421
[3] Berg, L.: On the asymptotics of nonlinear difference equations, Z. anal. Anwendungen 21, No. 4, 1061-1074 (2002) · Zbl 1030.39006
[4] Berg, L.; Stević, S.: Linear difference equations mod 2 with applications to nonlinear difference equations, J. difference equ. Appl. 14, No. 7, 693-704 (2008) · Zbl 1156.39003 · doi:10.1080/10236190701754891
[5] Çinar, C.; Stević, S.; Yalçinkaya, I.: On positive solutions of a reciprocal difference equation with minimum, J. appl. Math. & comput. 17, No. 1--2, 307-314 (2005) · Zbl 1074.39002 · doi:10.1007/BF02936057
[6] De La Sen, M.: About the properties of a modified generalized beverton--Holt equation in ecology models, Discrete dyn. Nat. soc. 2008 (2008) · Zbl 1148.92031 · doi:10.1155/2008/592950
[7] De La Sen, M.; Alonso-Quesada, S.: A control theory point of view on beverton--Holt equation in population dynamics and some of its generalizations, Appl. math. Comput. 199, No. 2, 464-481 (2008) · Zbl 1137.92034 · doi:10.1016/j.amc.2007.10.021
[8] De La Sen, M.; Alonso-Quesada, S.: Model-matching-based control of the beverton--Holt equation in ecology, Discrete dyn. Nat. soc. 2008 (2008) · Zbl 1149.92029 · doi:10.1155/2008/793512
[9] Elsayed, E. M.; Stević, S.: On the MAX-type equation xn+1=max{A/xn,xn-2}, Nonlinear anal. TMA 71, 910-922 (2009) · Zbl 1169.39003
[10] Feuer, J.: On the eventual periodicity of xn+1=max{1/xn,An/xn-1} with a period-four parameter, J. difference equ. Appl. 12, No. 5, 467-486 (2006) · Zbl 1095.39016 · doi:10.1080/10236190600574002
[11] Grove, E. A.; Ladas, G.: Periodicities in nonlinear difference equations, (2005) · Zbl 1078.39009
[12] Hu, H.: One recursion formula of second-order recurrent sequences, Ars combin. 88, 195-200 (2008) · Zbl 1224.11018
[13] Iričanin, B.: A global convergence result for a higher-order difference equation, Discrete dyn. Nat. soc. 2007 (2007)
[14] Iričanin, B.: Dynamics of a class of higher order difference equations, Discrete dyn. Nat. soc. 2007 (2007) · Zbl 1152.39005 · doi:10.1155/2007/73849
[15] Karakostas, G. L.: Convergence of a difference equation via the full limiting sequences method, Differ. equ. Dyn. syst. 1, No. 4, 289-294 (1993) · Zbl 0868.39002
[16] Massegú, J. R.: On the global periodicity of discrete dynamical systems and application to rational difference equations, J. math. Anal. appl. 343, No. 1, 182-189 (2008) · Zbl 1152.39008 · doi:10.1016/j.jmaa.2008.01.048
[17] Mishev, D.; Patula, W. T.; Voulov, H. D.: A reciprocal difference equation with maximum, Comput. math. Appl. 43, 1021-1026 (2002) · Zbl 1050.39015 · doi:10.1016/S0898-1221(02)80010-4
[18] Mishkis, A. D.: On some problems of the theory of differential equations with deviating argument, Uspekhi mat. Nauk 32:2, No. 194, 173-202 (1977)
[19] Patula, W. T.; Voulov, H. D.: On a MAX type recurrence relation with periodic coefficients, J. difference equ. Appl. 10, No. 3, 329-338 (2004) · Zbl 1050.39017 · doi:10.1080/10236190310001659741
[20] Pielou, E. C.: Population and community ecology, (1974) · Zbl 0349.92024
[21] Popov, E. P.: Automatic regulation and control, (1966)
[22] Stević, S.: Behaviour of the positive solutions of the generalized beddington--Holt equation, Panamer. math. J. 10, No. 4, 77-85 (2000) · Zbl 1039.39005
[23] Stević, S.: Asymptotic behaviour of a sequence defined by iteration with applications, Colloq. math. 93, No. 2, 267-276 (2002) · Zbl 1029.39006 · doi:10.4064/cm93-2-6
[24] Stević, S.: Asymptotic behaviour of a nonlinear difference equation, Indian J. Pure appl. Math. 34, No. 12, 1681-1687 (2003) · Zbl 1049.39012
[25] Stević, S.: On the recursive sequence xn+1=(A/\prodi=0kxn-i)+(1/\prodj=k+22(k+1)xn-j), Taiwanese J. Math. 7, No. 2, 249-259 (2003)
[26] S. Stević, Some open problems and conjectures on difference equations. http://www.mi.sanu.ac.yu/colloquiums/mathcoll_programs/mathcoll.apr2004.htm
[27] Stević, S.: On the recursive sequence xn+1=(${\alpha}+{\beta}$xn-k)/$f(xn,\dots ,xn-k+1)$, Taiwanese J. Math. 9, No. 4, 583-593 (2005) · Zbl 1100.39014
[28] Stević, S.: A short proof of the cushing--henson conjecture, Discrete dyn. Nat. soc. 2006 (2006) · Zbl 1149.39300 · doi:10.1155/DDNS/2006/37264
[29] Stević, S.: Asymptotic behaviour of a class of nonlinear difference equations, Discrete dyn. Nat. soc. (2006) · Zbl 1121.39006
[30] Stević, S.: On positive solutions of a (k+1)-th order difference equation, Appl. math. Lett. 19, No. 5, 427-431 (2006) · Zbl 1095.39010 · doi:10.1016/j.aml.2005.05.014
[31] Stević, S.: Asymptotics of some classes of higher order difference equations, Discrete dyn. Nat. soc. 2007 (2007) · Zbl 1152.39011 · doi:10.1155/2007/13737
[32] S. Stević, Boundedness character of a max-type difference equation, in: Conference in Honour of Allan Peterson, Book of Abstracts, Novacella, Italy, July 26 - August 02, 2007, p. 28
[33] Stević, S.: On the recursive sequence xn=1+(\sumi=$1k{\alpha}$ixn-pi/\sumj=$1m{\beta}$jxn-qj), Discrete dyn. Nat. soc. 2007 (2007)
[34] Stević, S.: Boundedness and global stability of a higher-order difference equation, J. difference equ. Appl. 14, No. 10--11, 1035-1044 (2008) · Zbl 1161.39011 · doi:10.1080/10236190802332258
[35] S. Stević, On behavior of a class of difference equations with maximum, in: Mathematical Models in Engineering, Biology and Medicine (Conference on Boundary Value Problems. Book of abstracts). Santiago de Compostela, Spain, September 16--19, 2008, p. 35
[36] Stević, S.: On the difference equation $xn+1={\alpha}$+(xn-1/xn), Comput. math. Appl. 56, No. 5, 1159-1171 (2008) · Zbl 1155.39305 · doi:10.1016/j.camwa.2008.02.017
[37] Stević, S.: On the recursive sequence xn+1=max${c,xnp/xn-1p}$, Appl. math. Lett. 21, No. 8, 791-796 (2008)$ · Zbl 1152.39012
[38] S. Stević, Some results on max-type difference equations, The Modelling of Nonlinear Processes and Systems (International Science Conference. Book of abstracts. Moscow), Russia, October 14--18, 2008, p. 140
[39] Stević, S.: Boundedness character of a class of difference equations, Nonlinear anal. TMA 70, 839-848 (2009) · Zbl 1162.39011 · doi:10.1016/j.na.2008.01.014
[40] Stević, S.: Global stability of a difference equation with maximum, Appl. math. Comput. 210, 525-529 (2009) · Zbl 1167.39007 · doi:10.1016/j.amc.2009.01.050
[41] Szalkai, I.: On the periodicity of the sequence xn+1=max{A0/xn,$\dots $,Ak/xn-k}, J. difference equ. Appl. 5, 25-29 (1999)
[42] Sun, F.: On the asymptotic behavior of a difference equation with maximum, Discrete dyn. Nat. soc. 2008 (2008) · Zbl 1155.39008 · doi:10.1155/2008/243291
[43] Voulov, H. D.: On the periodic nature of the solutions of the reciprocal difference equation with maximum, J. math. Anal. appl. 296, No. 1, 32-43 (2004) · Zbl 1053.39023 · doi:10.1016/j.jmaa.2004.02.054
[44] Voulov, H. D.: On a difference equation with periodic coefficients, J. difference equ. Appl. 13, No. 5, 443-452 (2007) · Zbl 1121.39011 · doi:10.1080/10236190701264651
[45] Yalçinkaya, I.; Iričanin, B. D.; Çinar, C.: On a MAX-type difference equation, Discrete dyn. Nat. soc. 2007 (2007) · Zbl 1152.39016 · doi:10.1155/2007/47264
[46] Yang, X.; Sun, F.; Tang, Y. Y.: A new part-metric-related inequality chain and an application, Discrete dyn. Nat. soc. 2008 (2008) · Zbl 1151.26316 · doi:10.1155/2008/193872
[47] Yang, Y.; Yang, X.: On the diference equation xn+1=(pxn-s+xn-t)/(qxn-s+xn-t), Appl. math. Comput. 203, No. 2, 903-907 (2008) · Zbl 1162.39015 · doi:10.1016/j.amc.2008.03.023