Estimates For Eigenvalues Of The Buckling Problem Of Arbitrary Bounded Domain In Euclidean Spaces

In the1960s, Mathematicians draw a lot of useful conclusions on the research of differential operators about the Riemannian manifold, especially for the eigenvalue problem of Laplace operators. The conclusion drawn by M. Kac in1966was its main representative, and these conclusions contributed to the research and development of the eigenvalue problem. The eigenvalue problem of differential operators on the mani-fold is still an important subject analysis in manifold so far. The research results of the eigenvalue problems are used in a wide range of applications, mainly in mathematics and physics, and other disciplines.The problem which meets the following condition problem is called Buckling problem: Where Ω is a smooth connected bounded domain in an n-dimensional Euclidean space,△is the Laplace operator, n is an unit normal vector on the boundary αΩ.This paper uses Wang ang Xia’s method in their paper for "Eigenvalue estimat-ing on Spherical Domains" to obtain universal inequalities that the k+1th eigenvalues was estimatesd by the front k eigenvalues of biharmonic operator on smooth edge con-nected with a bounded area in n-dimensional Euclidean space.