Inequalities for eigenvalues of the poly-Laplacian with arbitrary order on spherical domains

Abstract

In this paper, we are devoted to the study of universal inequalities for eigenvalues of the poly-Laplacian with arbitrary order on bounded domains in $S^n\left(1\right)$, respectively, and then establish some new universal inequalities that are different from those already present in the literature. In particular, our results can reveal the relationship between the $(k+1)$-th eigenvalue and the first k eigenvalues relatively quickly, and some methods used in this paper might be applied to other eigenvalue problems.