Korean J. Math. Vol. 23 No. 2 (2015) pp.259-267
DOI: https://doi.org/10.11568/kjm.2015.23.2.259

Dirichlet boundary value problem for a class of the noncooperative elliptic system

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Published: Jun 30, 2015
Keywords:
Noncooperative elliptic system, critical Sobolev expo- nents nonlinear term, eigenvalue problem of the matrix.
Mathematics Subject Classification:
35J50, 35J55.

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Tacksun Jung
Department of Mathematics Kunsan National University Kunsan 573-701, Korea
Q-Heung Choi
Department of Mathematics Education Inha University Incheon 402-751, Korea

Abstract

This paper is devoted to investigate the existence of the solutions for a class of the noncooperative elliptic system involving critical Sobolev exponents. We show the existence of the negative solution for the problem. We show the existence of the unique negative solution for the system of the linear part of the problem under some conditions, which is also the negative solution of the nonlinear problem. We also consider the eigenvalue problem of the matrix.


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Supporting Agencies

†This work was supported by Basic Science Research Program through the Na- tional Research Foundation of Korea(NRF) funded by the Ministry of Education Science and Technology (KRF-2013010343).

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