Research On The Nonlinear Eigenvalue Problem Of A Four Order Ordinary Differtial Operater

The present paper will research on the nonlinear eigenvalue problem of a four order differtial operatorwhere x∈[0,π] and h(x,u,u',u",u"') is a real valued continuous function which defined over [0,π]×(?)×(?)×(?)×(?). The spectrum theory of the symmetrical fully continuous operator can give the results of linear eigenvalue problem. Linearizing nonlinear eigenvalue problem and using Schauder fixed point theorem, the fixed point of this mapping can be obtained. While, this fixed point is just the solution of the nonlinear eigenvalue problem. Then eigenvalue existence is justified. And the correspnding result of nonlinear eigenvalue problem can be obtained by restorting to the linear problem result.