Korean J. Math. Vol. 23 No. 4 (2015) pp.619-630
DOI: https://doi.org/10.11568/kjm.2015.23.4.619

Multiplicity result of the solutions for a class of the elliptic systems with subcritical Sobolev exponents

Article Sidebar

PDF
Published: Dec 30, 2015
Keywords:
Cooperative elliptic system, subcritical Sobolev exponents nonlinear term, variational method, mountain pass theorem.
Mathematics Subject Classification:
35J50, 35J55

Main Article Content

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 multiple solutions for a class of the cooperative elliptic system involving subcritical Sobolev exponents on the bounded domain with smooth boundary. We first show the uniqueness and the negativity of the solution for the linear system of the problem via the direct calculation. We next use the variational method and the mountain pass theorem in the critical point theory.


Article Details

Supporting Agencies

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

References

[1] C. O. Alves, D. C. De Morais Filho and M. A. Souto, On systems of equations involving subcritical or critical Sobolev exponents, Nonlinear Analysis, Theory, Meth. and Appl. 42 (2000), 771–787. Google Scholar

[2] 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. Google Scholar

[3] K. C. Chang, Ambrosetti-Prodi type results in elliptic systems, Nonlinear Anal- ysis TMA. 51 (2002), 553–566. Google Scholar

[4] D. G. de Figueiredo, Lectures on boundary value problems of the Ambrosetti- Prodi type, 12 Semin ario Brasileiro de An alise, 232-292 (October 1980). Google Scholar

[5] Rabinowitz, P. H., Minimax methods in critical point theory with applications to differential equations, CBMS. Regional conf. Ser. Math. 65, Amer. Math. Soc., Providence, Rhode Island (1986). Google Scholar