Dirichlet boundary value problem for a class of the noncooperative elliptic system
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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.
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.
참고문헌 (7)
- A. Ambrosetti, "On the inversion of some di erential mappings with singularities between Banach spaces", Ann. Mat. Pura. Appl, 93, pp.231~246 (1972)
- K. C. Chang, "Ambrosetti-Prodi type results in elliptic systems", Nonlinear Anal-ysis TMA, 51, pp.553~566 (2002)
- D. G. de Figueiredo, "Lectures on boundary value problems of the Ambrosetti-Prodi type", 12 Seminario Brasileiro de Analise, 232(292) (1980)
- D. G. de Figueiredo, "On the superlinear Ambrosetti-Prodi Problem", MRC Tech. Rep, 2522 (1983)
- D. G. de Figueiredo, "Critical superlinear Ambrosetti-Prodi prob-lems, Top", Methods in Nonlinear Analysis, 14(1), pp.59~80 (1999)
- A. M. Micheletti, "Multiple nontrivial solutions for a oating beam equation via critical point theory", J. Di erential Equations, 170, pp.157~179 (2001)
- 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), pp.1655~1668 (1996)