Eigenvalue inequalities for the buckling problem of the drifting Laplacian on Ricci solitons

In this paper, we investigate the buckling problem of the drifting Laplacian and get a general inequality for its eigenvalues on a bounded connected domain in complete Ricci solitons supporting a special function. By applying this general inequality, we obtain some universal inequalities for eigenvalues of the same problem on bounded connected domains in the Gaussian shrinking solitons and some general product solitons.