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

Tacksun Jung, Q-Heung Choi

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.

Keywords


Noncooperative elliptic system, critical Sobolev expo- nents nonlinear term, eigenvalue problem of the matrix.

Subject classification

35J50, 35J55.

Sponsor(s)

†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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