Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
권호 표지
DOI QR코드

DOI QR Code

DIRICHLET BOUNDARY VALUE PROBLEM FOR A CLASS OF THE NONCOOPERATIVE ELLIPTIC SYSTEM

  • JUNG, TACKSUN (Department of Mathematics Kunsan National University) ;
  • CHOI, Q-HEUNG (Department of Mathematics Education Inha University)
  • Received : 2015.01.14
  • Accepted : 2015.06.02
  • Published : 2015.06.30
Download PDF
⟨ Previous Next ⟩

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

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

References

  1. A. Ambrosetti and G. Prodi, On the inversion of some differential mappings with singularities between Banach spaces, Ann. Mat. Pura. Appl. 93 (1972), 231-246. https://doi.org/10.1007/BF02412022
  2. K. C. Chang, Ambrosetti-Prodi type results in elliptic systems, Nonlinear Analysis TMA. 51 (2002), 553-566. https://doi.org/10.1016/S0362-546X(01)00146-8
  3. D. G. de Figueiredo, Lectures on boundary value problems of the Ambrosetti-Prodi type, 12 Seminario Brasileiro de Analise, 232-292 (October 1980).
  4. D. G. de Figueiredo, On the superlinear Ambrosetti-Prodi Problem, MRC Tech. Rep 2522, May, (1983).
  5. D. G. de Figueiredo and Y. Jianfu, Critical superlinear Ambrosetti-Prodi prob- lems, Top. Methods in Nonlinear Analysis, 14 (1) (1999), 59-80. https://doi.org/10.12775/TMNA.1999.022
  6. A. M. Micheletti and C. Saccon, Multiple nontrivial solutions for a floating beam equation via critical point theory, J. Differential Equations 170 (2001), 157-179. https://doi.org/10.1006/jdeq.2000.3820
  7. D. C. de Morais Filho, A Variational approach to an Ambrosetti-Prodi type problem for a system of elliptic equations, Nonlinear Analysis, TMA. 26 (10) (1996), 1655-1668. https://doi.org/10.1016/0362-546X(95)00028-T