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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.

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References

  1. 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. 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

    MathSciNet  Article  MATH  Google Scholar 

  3. 3.

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

    Google Scholar 

  4. 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. 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

    MathSciNet  Article  MATH  Google Scholar 

  6. 6.

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

    Google Scholar 

  7. 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

    MathSciNet  Article  MATH  Google Scholar 

  8. 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. 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. 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

    MathSciNet  Article  MATH  Google Scholar 

  11. 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. 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

    MathSciNet  Article  MATH  Google Scholar 

  13. 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.

    Google Scholar 

  14. 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.

    Google Scholar 

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Affiliations

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

    Rodica Luca

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  1. Rodica Luca
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Correspondence to Rodica Luca.

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

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Keywords

  • Differential Equation
  • Hilbert Space
  • Partial Differential Equation
  • Initial Data
  • Ordinary Differential Equation