黎曼流形上漂移薛定谔算子的加权特征值估计

Inequalities for weighted eigenvalues of the drifting Schrodinger operator on Riemannian manifolds

研究了黎曼流形上漂移薛定谔算子-Δ_φ+V的加权特征值估计问题,利用试验函数方法得到了特征值的杨洪仓型不等式,同时得到了高阶特征值的上界估计,将已有文献结果推广到更一般的情形.

The Dirichlet weighted eigenvalue problem of the operator -Δφ＋V on compact Riemannian manifolds is investigated,where Δφis the drifting Laplacian operator on compact Riemannian manifolds.A yang-type inequality of this problem is established.Estimates for upper bounds of higher order eigenvalues are also obtained.