Skip to main content
Advances in Continuous and Discrete Models

Theory and Modern Applications

Download PDF
  • Research Article
  • Open access
  • Published:

Boundary value problems for functional difference equations on infinite intervals

Advances in Difference Equations volume 2006, Article number: 031283 (2006) Cite this article

Abstract

A general method for solving boundary value problems associated to functional difference systems on the discrete half-line is presented and applied in studying the existence of positive unbounded solutions for a system of two coupled nonlinear difference equations. A further example, illustrating the method, completes the paper.

[12345678910111213141516171819]

References

  1. Agarwal RP: Difference Equations and Inequalities. Theory, Methods, and Applications, Monographs and Textbooks in Pure and Applied Mathematics. Volume 228. 2nd edition. Marcel Dekker, New York; 2000:xvi+971.

    Google Scholar 

  2. Agarwal RP, O'Regan D: Existence and approximation of solutions of non-linear discrete systems on infinite intervals. Mathematical Methods in the Applied Sciences 1999,22(1):91–99. 10.1002/(SICI)1099-1476(19990110)22:1<91::AID-MMA22>3.0.CO;2-F

    Article  MathSciNet  MATH  Google Scholar 

  3. Agarwal RP, O'Regan D: Infinite Interval Problems for Differential, Difference and Integral Equations. Kluwer Academic, Dordrecht; 2001:x+341.

    Book  MATH  Google Scholar 

  4. Agarwal RP, O'Regan D: Nonlinear Urysohn discrete equations on the infinite interval: a fixed-point approach. Computers & Mathematics with Applications. An International Journal 2001,42(3–5):273–281. 10.1016/S0898-1221(01)00152-3

    Article  MathSciNet  MATH  Google Scholar 

  5. Agarwal RP, O'Regan D, Wong PJY: Positive Solutions of Differential, Difference and Integral Equations. Kluwer Academic, Dordrecht; 1999:xii+417.

    Book  MATH  Google Scholar 

  6. Cabada A: Extremal solutions for the difference φ -Laplacian problem with nonlinear functional boundary conditions. Computers & Mathematics with Applications. An International Journal 2001,42(3–5):593–601. 10.1016/S0898-1221(01)00179-1

    Article  MathSciNet  MATH  Google Scholar 

  7. Cecchi M, Došlá Z, Marini M: Positive decreasing solutions of quasi-linear difference equations. Computers & Mathematics with Applications. An International Journal 2001,42(10–11):1401–1410. 10.1016/S0898-1221(01)00249-8

    Article  MathSciNet  MATH  Google Scholar 

  8. Cecchi M, Furi M, Marini M: On continuity and compactness of some nonlinear operators associated with differential equations in noncompact intervals. Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods 1985,9(2):171–180.

    Article  MathSciNet  MATH  Google Scholar 

  9. Graef JR, Henderson J: Double solutions of boundary value problems for 2mth-order differential equations and difference equations. Computers & Mathematics with Applications. An International Journal 2003,45(6–9):873–885. 10.1016/S0898-1221(03)00063-4

    Article  MathSciNet  MATH  Google Scholar 

  10. Graef JR, Qian C, Yang B: A three point boundary value problem for nonlinear fourth order differential equations. Journal of Mathematical Analysis and Applications 2003,287(1):217–233. 10.1016/S0022-247X(03)00545-6

    Article  MathSciNet  MATH  Google Scholar 

  11. Marić V: Regular Variation and Differential Equations, Lecture Notes in Mathematics. Volume 1726. Springer, Berlin; 2000:x+127.

    MATH  Google Scholar 

  12. Marini M, Matucci S, Řehák P: Oscillation of coupled nonlinear discrete systems. Journal of Mathematical Analysis and Applications 2004,295(2):459–472. 10.1016/j.jmaa.2004.03.013

    Article  MathSciNet  MATH  Google Scholar 

  13. Medina R, Pinto M: Convergent solutions of functional difference equations. Journal of Difference Equations and Applications 1998,3(3–4):277–288.

    Article  MathSciNet  MATH  Google Scholar 

  14. Migda M, Musielak A, Schmeidel E: On a class of fourth-order nonlinear difference equations. Advances in Difference Equations 2004,2004(1):23–36. 10.1155/S1687183904308083

    Article  MathSciNet  MATH  Google Scholar 

  15. Patula WT: Growth and oscillation properties of second order linear difference equations. SIAM Journal on Mathematical Analysis 1979,10(1):55–61. 10.1137/0510006

    Article  MathSciNet  MATH  Google Scholar 

  16. Rodriguez J: Nonlinear discrete systems with global boundary conditions. Journal of Mathematical Analysis and Applications 2003,286(2):782–794. 10.1016/S0022-247X(03)00536-5

    Article  MathSciNet  MATH  Google Scholar 

  17. Schmeidel E, Szmanda B: Oscillatory and asymptotic behavior of certain difference equation. Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods 2001,47(7):4731–4742.

    Article  MathSciNet  MATH  Google Scholar 

  18. Wang X, Liao L: Oscillation for even-order delay difference equations with unstable type. Applied Mathematics and Computation 2004,153(1):289–299. 10.1016/S0096-3003(03)00717-3

    Article  MathSciNet  MATH  Google Scholar 

  19. Yan J, Liu B: Oscillatory and asymptotic behaviour of fourth order nonlinear difference equations. Acta Mathematica Sinica. New Series 1997,13(1):105–115. 10.1007/BF02560530

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electronics and Telecommunications, University of Florence, Florence, I-50139, Italy

    Mauro Marini & Serena Matucci

  2. Mathematical Institute, Academy of Sciences of the Czech Republic, Brno, CZ-61662, Czech Republic

    Pavel Řehák

Authors
  1. Mauro Marini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Serena Matucci
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pavel Řehák
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mauro Marini.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and permissions

About this article

Cite this article

Marini, M., Matucci, S. & Řehák, P. Boundary value problems for functional difference equations on infinite intervals. Adv Differ Equ 2006, 031283 (2006). https://doi.org/10.1155/ADE/2006/31283

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/ADE/2006/31283

Keywords