Inequalities for Eigenvalues of the Buckling Problem of Higher Orders

Abstract

This paper studies eigenvalues of the buckling problem of arbitrary order on compact domains in Euclidean spaces and spheres. We prove universal bounds for the $k$-th eigenvalue in terms of the lower ones independent of the domains. Our results strengthens the recent work by Jost, Li-Jost, Wang and Xia and generalizes Cheng-Yang's recent estimates on the buckling eigenvalues of order two to arbitrary order.

The authors understood that Qing-ming Cheng and Qi Xuerong have also obtained the same results. The four authors have decided to write a joint paper and so this paper has been withdraw