Yang-type inequalities for weighted eigenvalues of a second order uniformly elliptic operator with a nonnegative potential
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Abstract:
In this paper, we investigate the Dirichlet weighted eigenvalue problem of a second order uniformly elliptic operator with a nonnegative potential on a bounded domain $\Omega \subset \mathbb {R}^n$. First, we prove a general inequality of eigenvalues for this problem. Then, by using this general inequality, we obtain Yang-type inequalities which give universal upper bounds for eigenvalues. An explicit estimate for the gaps of any two consecutive eigenvalues is also derived. Our results contain and extend the previous results for eigenvalues of the Laplacian, the Schrödinger operator and the second order elliptic operator on a bounded domain $\Omega \subset \mathbb {R}^n$.References
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Additional Information
- He-Jun Sun
- Affiliation: Department of Applied Mathematics, College of Science, Nanjing University of Science and Technology, Nanjing 210094, People’s Republic of China
- Email: hejunsun@163.com
- Received by editor(s): August 22, 2009
- Received by editor(s) in revised form: November 18, 2009
- Published electronically: March 16, 2010
- Communicated by: Matthew J. Gursky
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 2827-2837
- MSC (2010): Primary 35P15, 58C40; Secondary 58J50
- DOI: https://doi.org/10.1090/S0002-9939-10-10321-9
- MathSciNet review: 2644896