On Dirichlet Problem Of Biharmonic Equations With Constraints

This dissertation consider the following problems.where Ω(?)RN(N≥ 5)is a bounded domain with smooth boundary(?)Ω,Δ2 is the biharmonic operator,and λ is a constant.Suppose that λk is the kth eigenvalue ofΔ2 biharmonic operator under the above boundary conditions.The dissertation is divided into four parts:In chapter 1,we present some propositions and definitions for further use.In chapter 2,we obtain a nontrivial solution when λ less than or equal to λ1.In chapter 3,we discuss the multiplicity of equations when λ belongs to the interval(λk,λk+1).Then we use the Z2 index and prove that there are infinitely many solutions to the equation.In the fourth chapter,we summarize the work of this thesis and points out some problems to be solved.