On the recursive sequence Xn+1=alfa+Xn-k:f(Xn,....Xn-k+1)

• Autorzy: Karakostas G. , Stević S.
• Języki publikacji: EN

Abstrakty

EN

The boundedness, global attractivity, oscillatory and asymptotic periodicity of the nonnegative solutions of the difference equation of the form Xn+l=alfa+Xn-k:f(Xn,....Xn-k+1, n=0, 1, ..... is investigated, where alfa > 0, k is an element of N and f : [0,infinity)- (0,infinity)k is a continuous function nondecreasing in each variable.

Słowa kluczowe

EN

recursive sequence; continuous functions; difference equation; positive solution; global attractivity; asymptotic periodicity

PL

ciągi rekusywne; funkcje ciągłe; równania różniczkowe; rozwiązania pozytywne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 3
• Strony: 595--610
• Opis fizyczny: Bibliogr. 26 poz.

Twórcy

autor

Karakostas G.

• Department of Mathematics University of Ioannina 451 10 Ioannina, Greece

autor

Stević S.

• Mathematical Institute of the Serbian Academy of Science , Knez Mihailova 35/1 , 11000 Beograd, Serbia

Bibliografia

• [1] A. M. Amleh , E. A. Grove, G. Ladas and D. A. Georgiou , On the recursive sequence yn+1 = α + J. Math. Anal. Appi. 233 (1999), 790-798.
• [2] L. Berg, On the asymptotics of nonlinear difference equations, Z. Anal. Anwend. 21 (2002), 1061-1074.
• [3] H. E l-Metwally , E. A. Grove and G. Ladas, A global convergence result with applications to periodic solutions, J. Math. Anal. Appi. 245 (2000), 161-170.
• [4] C. H. Gibbons , M. R. S. Kulenovic and G. Ladas, On the recursive sequence x n + i = , Math. Sei. Res. Hot-Line 4 (2) (2000), 1-11.
• [5] C. H. Gibbons, M. R. S. Kulenovic, G. Ladas and H. D. Voulov, On the trichotomy character of xn+1 = (…), J. Differ Equations Appi. 8 (1) (2002), 75-92.
• [6] G. L. Karakostas , A discrete semi-flow in the space of sequences and study of convergence of sequenses defined by difference equations, M. E. Greek Math. Soc. 30 (1989), 66-74.
• [7] G. L. Karakostas , Convergence of a difference equation via the full limiting sequences method, Differ. Equ. Dyn. Syst. 1 (4) (1993), 289-294.
• [8] G. L. Karakostas , Asymptotic 2-periodic difference equations with diagonally self-invertible responces, J. Differ. Equations Appi. 6 (2000), 329-335.
• [9] G. L. Karakostas , On the asymptotic behavior of the difference equation xn+i =xn(a-F(xn-1))F(xn-2), Math. Sei. Res. Hot-Line 12 (2002), 558-572.
• [10] G. Karakostas and S. Stevic, On the recursive sequence xn+\ = Af{xn)+f{xn-i), Appi. Anal. 83 (2004), 309-323.
• [11] G. Karakostas and S. Stevic, Slowly varying solutions of the difference equations xn+1 = f(xn, … , xn-k+1)) + g(n, xn , … , xn-k+1), J·Differ. Equations Appi. 10 (3) (2004), 249-255.
• [12] V. L. Kocic and G. Ladas, Global Behaviour of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic Publishers, Dordrecht, 1993.
• [13] S. Stevic, Behaviour of the positive solutions of the generalized Beddington-Holt equation, Panamer. Math. J. 10 (4) (2000), 77-85.
• [14] S. Stevic, A generalization of the Copson's theorem concerning sequences which satisfy a linear inequality, Indian J. Math. 43 (3) (2001), 277-282.
• [15] S. Stevic, On the recursive sequence xn+i = (…) Int. J. Math. Math. Sci. 27 (1) (2001), 1-6.
• [16] S. Stevic, A global convergence result, Indian J. Math. 44 (3) (2002), 361-368.
• [17] S. Stevic, A global convergence results with applications to periodic s olutions, IndianJ. Pure Appi. Math. 33 (1) (2002), 45-53.
• [18] S. Stevic, A note on the difference equation xn +i = Σ(…), J. Differ. Equations Appi. 8 (7) (2002), 641-647.
• [19] S. Stevic, Asymptotic behaviour of a sequence defined by iteration with applications, Colloq. Math. 93 (2) (2002), 267-276.
• [20] S. Stevic, On the recursive sequence xn +i = g(xn,xn-i)/(A + Xn), Appi. Math. Lett. 15 (2002), 305-308.
• [21] S. Stevic, On the recursive sequence i n + i = Xn-i/g(xn), Taiwanese J. Math. 6 (3) (2002), 405-414.
• [22] S. Stevic, On the recursive sequence xn+i = (…) , Indian J. Pure Appi. Math. 33 (12) (2002), 1767-1774.
• [23] S. Stevic, On the recursive sequence xn+i = (…) , Taiwanese J. Math. 7 (2) (2003), 249-259.
• [24] S. Stevic, On the recursive sequence i n + i = a n + Ih Dynam. Contin. Discrete Impuls. Systems 10a (6) (2003), 911-917.
• [25] S. Stevic, Periodic character of a class of difference equation, J. Differ. Equations Appi. 10 (6) (2004), 615-619.
• [26] S. Stevic, A note on periodic character of a difference equation, J. Differ. Equations Appi. 10 (10) (2004), 92^-932.