Skip to main content
Advances in Continuous and Discrete Models

Theory and Modern Applications

Download PDF
  • Research Article
  • Open access
  • Published:

Existence for a class of discrete hyperbolic problems

Advances in Difference Equations volume 2006, Article number: 089260 (2006) Cite this article

Abstract

We investigate the existence and uniqueness of solutions to a class of discrete hyperbolic systems with some nonlinear extreme conditions and initial data, in a real Hilbert space.

[12345678910111213141234567891011121314]

References

  1. Agarwal RP, O'Regan D: Difference equations in abstract spaces. Journal of Australian Mathematical Society. Series A 1998,64(2):277–284. 10.1017/S1446788700001762

    Article  MathSciNet  MATH  Google Scholar 

  2. Agarwal RP, O'Regan D, Lakshmikantham V: Discrete second order inclusions. Journal of Difference Equations and Applications 2003,9(10):879–885. 10.1080/1023619031000097044

    Article  MathSciNet  MATH  Google Scholar 

  3. Barbu V: Nonlinear Semigroups and Differential Equations in Banach Spaces. Noordhoff, Leiden; 1976:352.

    Book  Google Scholar 

  4. Barbu V: Nonlinear boundary-value problems for a class of hyperbolic systems. Revue Roumaine de Mathématiques Pures et Appliquées 1977,22(2):155–168.

    MathSciNet  MATH  Google Scholar 

  5. Barbu V, Moroşanu G: Existence for a nonlinear hyperbolic system. Nonlinear Analysis 1981,5(4):341–353. 10.1016/0362-546X(81)90019-5

    Article  MathSciNet  MATH  Google Scholar 

  6. Brézis H: Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland, Amsterdam; 1973:vi+183.

    MATH  Google Scholar 

  7. Cooke KL, Krumme DW: Differential-difference equations and nonlinear initial-boundary value problems for linear hyperbolic partial differential equations. Journal of Mathematical Analysis and Applications 1968,24(2):372–387. 10.1016/0022-247X(68)90038-3

    Article  MathSciNet  MATH  Google Scholar 

  8. Halanay A, Răsvan V: Frequency domain conditions for forced oscillations in difference systems. Revue Roumaine des Sciences Techniques. Série Électrotechnique et Énergétique 1979,24(1):141–148.

    MathSciNet  MATH  Google Scholar 

  9. Iftimie V: Sur un problème non linéaire pour un système hyperbolique. Revue Roumaine de Mathématiques Pures et Appliquées 1976,21(3):303–328.

    MathSciNet  MATH  Google Scholar 

  10. Liz E, Pituk M: Asymptotic estimates and exponential stability for higher-order monotone difference equations. Advances in Difference Equations 2005,2005(1):41–55. 10.1155/ADE.2005.41

    Article  MathSciNet  MATH  Google Scholar 

  11. Luca R: An existence result for a nonlinear hyperbolic system. Differential and Integral Equations 1995,8(4):887–900.

    MathSciNet  MATH  Google Scholar 

  12. Moroşanu G: Mixed problems for a class of nonlinear differential hyperbolic systems. Journal of Mathematical Analysis and Applications 1981,83(2):470–485. 10.1016/0022-247X(81)90136-0

    Article  MathSciNet  MATH  Google Scholar 

  13. Moroşanu G: Nonlinear Evolution Equations and Applications, Mathematics and Its Applications (East European Series). Volume 26. D. Reidel, Dordrecht; Editura Academiei, Bucharest; 1988:xii+340.

    MATH  Google Scholar 

  14. Rousseau A, Temam R, Tribbia J: Boundary conditions for an ocean related system with a small parameter. In Nonlinear Partial Differential Equations and Related Analysis, Contemporary Mathematics. Volume 371. American Mathematical Society, Rhode Island; 2005:231–263.

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, "Gheorghe Asachi" Technical University of Iaşi, Boulevard Carol I number 11, Iaşi, 700506, Romania

    Rodica Luca

Authors
  1. Rodica Luca
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rodica Luca.

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

Luca, R. Existence for a class of discrete hyperbolic problems. Adv Differ Equ 2006, 089260 (2006). https://doi.org/10.1155/ADE/2006/89260

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/ADE/2006/89260

Keywords