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Boundary value problems for functional difference equations on infinite intervals

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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.

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References

  1. 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.

  2. 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

  3. 3.

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

  4. 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

  5. 5.

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

  6. 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

  7. 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

  8. 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.

  9. 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

  10. 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

  11. 11.

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

  12. 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

  13. 13.

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

  14. 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

  15. 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

  16. 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

  17. 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.

  18. 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

  19. 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

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Correspondence to Mauro Marini.

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation