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.
Categories: math.AP