Estimates for eigenvalues of Laplacian operator with any order

【摘要】：正Let D be a bounded domain in an n-dimensional Euclidean space R~n.Assume that 0λ_1≤λ_2≤…≤λ_k≤…are the eigenvalues of the Dirichlet Laplacian operator with any order l: (-△)~lu=λu,in D u=■=…=■=0,on■■D. Then we obtain an upper bound of the(k+1)-th eigenvalueλ_(k+1)in terms of the first k eigenvalues.