# American Institute of Mathematical Sciences

February  2017, 6(2): 475-491. doi: 10.3934/cpaa.2017024

## Estimates for eigenvalues of a system of elliptic equations with drift and of bi-drifting laplacian

 1 School of Mathematics and Physics Science, Jingchu University of Technology, Jingmen, 448000, China 2 Departamento de Matemática, Universidade de Brasilia, 70910-900-Brasilia-DF, Brazil

Received  April 2016 Revised  October 2016 Published  January 2016

In this paper, we firstly study the eigenvalue problem of a systemof elliptic equations with drift and get some universal inequalities of PayneP′olya-Weinberger-Yang type on a bounded domain in Euclidean spaces and inGaussian shrinking solitons. Furthermore, we study two kinds of the clampedplate problems and the buckling problems for the bi-drifting Laplacian and getsome sharp lower bounds for the first eigenvalue for these eigenvalue problemon compact manifolds with boundary and positive m-weighted Ricci curvatureor on compact manifolds with boundary under some condition on the weightedRicci curvature.

Citation: Feng Du, Adriano Cavalcante Bezerra. Estimates for eigenvalues of a system of elliptic equations with drift and of bi-drifting laplacian. Communications on Pure & Applied Analysis, 2017, 6 (2) : 475-491. doi: 10.3934/cpaa.2017024
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