Fourth order elliptic system with dirichlet boundary condition

Abstract

Abstract We investigate the multiplicity of the solutions of the fourth order elliptic system with Dirichlet boundary condition. We get two theorems. One theorem is that the fourth order elliptic system has at least two nontrivial solutions when λ k < c < λ k+1 and λ k+n (λ k+n - c) < a + b < λ k+n+1(λ k+n+1 - c). We prove this result by the critical point theory and the variation of linking method. The other theorem is that the system has a unique nontrivial solution when λ k < c < λ k+1 and λ k (λ k - c) < 0, a+b < λ k+1(λ k+1 - c). We prove this result by the contraction mapping principle on the Banach space. AMS Mathematics Subject Classification: 35J30, 35J48, 35J50

Keywords

• Fourth order elliptic system
• fourth order elliptic equation
• variation linking theorem
• contraction mapping principle