Advances in Difference Equations

Impact Factor 0.335

Advances in Difference Equations Cover Image
Research Article
Open Access

Existence for a class of discrete hyperbolic problems

Advances in Difference Equations20062006:089260

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

©  Rodica Luca 2006

Received: 1 November 2005

Accepted: 7 April 2006

Published: 31 August 2006

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]

Authors’ Affiliations

(1)
Department of Mathematics, "Gheorghe Asachi" Technical University of Iaşi

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/S1446788700001762View ArticleMathSciNetMATHGoogle Scholar
  2. Agarwal RP, O'Regan D, Lakshmikantham V: Discrete second order inclusions. Journal of Difference Equations and Applications 2003,9(10):879–885. 10.1080/1023619031000097044MathSciNetView ArticleMATHGoogle Scholar
  3. Barbu V: Nonlinear Semigroups and Differential Equations in Banach Spaces. Noordhoff, Leiden; 1976:352.View ArticleGoogle 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.MathSciNetMATHGoogle Scholar
  5. Barbu V, Moroşanu G: Existence for a nonlinear hyperbolic system. Nonlinear Analysis 1981,5(4):341–353. 10.1016/0362-546X(81)90019-5MathSciNetView ArticleMATHGoogle Scholar
  6. Brézis H: Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland, Amsterdam; 1973:vi+183.MATHGoogle 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)90038-3MathSciNetView ArticleMATHGoogle 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.MathSciNetMATHGoogle 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.MathSciNetMATHGoogle 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.2005.41MathSciNetView ArticleMATHGoogle Scholar
  11. Luca R: An existence result for a nonlinear hyperbolic system. Differential and Integral Equations 1995,8(4):887–900.MathSciNetMATHGoogle 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)90136-0MathSciNetView ArticleMATHGoogle 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.MATHGoogle 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.View ArticleGoogle Scholar

Copyright

© Rodica Luca 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.