At least two solutions for the asymmetric beam system with critical growth
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We consider the multiplicity of the solutions for a class of a system of critical growth beam equations with periodic condition on t and Dirichlet boundary condition [수식]where α, β >1 are real constants, u_+ = max{u,0}, φ(_00) is the eigenfunction corresponding to the positive eigenvalue λ(_00)=1 of the eigenvalue problem u(_tt) + u(_xxxx) = λ(_mn)u. We show that the system has a positive solution under suitable conditions on the matrix A =[수식], s > 0, t > 0, and next show that the system has another solution for the same conditions on A by the linking arguments.
Abstract
We consider the multiplicity of the solutions for a class of a system of critical growth beam equations with periodic condition on t and Dirichlet boundary condition [수식]where α, β >1 are real constants, u_+ = max{u,0}, φ(_00) is the eigenfunction corresponding to the positive eigenvalue λ(_00)=1 of the eigenvalue problem u(_tt) + u(_xxxx) = λ(_mn)u. We show that the system has a positive solution under suitable conditions on the matrix A =[수식], s > 0, t > 0, and next show that the system has another solution for the same conditions on A by the linking arguments.
참고문헌 (5)
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