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CONTRACTION MAPPING PRINCIPLE AND ITS APPLICATION TO UNIQUENESS RESULTS FOR THE SYSTEM OF THE WAVE EQUATIONS
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  • Journal title : Honam Mathematical Journal
  • Volume 30, Issue 1,  2008, pp.197-203
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2008.30.1.197
 Title & Authors
CONTRACTION MAPPING PRINCIPLE AND ITS APPLICATION TO UNIQUENESS RESULTS FOR THE SYSTEM OF THE WAVE EQUATIONS
Jung, Tack-Sun; Choi, Q-Heung;
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 Abstract
We show the existence of the unique solution of the following system of the nonlinear wave equations with Dirichlet boundary conditions and periodic conditions under some conditions in , in , where = max{u, 0}, s, t R, is the eigenfunction corresponding to the positive eigenvalue of the wave operator. We first show that the system has a positive solution or a negative solution depending on the sand t, and then prove the uniqueness theorem by the contraction mapping principle on the Banach space.
 Keywords
System of wave equations;jumping nonlinearity;eigenvalues of the matrix;contraction mapping principle;Dirichlet boundary condition;
 Language
English
 Cited by
 References
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