Multiplicity result of the solutions for a class of the elliptic systems with subcritical Sobolev exponents
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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.
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.
참고문헌 (5)
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- 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)
- Rabinowitz, P. H., "Minimax methods in critical point theory with applications to di erential equations", CBMS. Regional conf. Ser. Math, 65 (1986), Amer. Math. Soc.