CONTRACTION MAPPING PRINCIPLE AND ITS APPLICATION TO UNIQUENESS RESULTS FOR THE SYSTEM OF THE WAVE EQUATIONS

- 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;

Jung, Tack-Sun; Choi, Q-Heung;

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

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