The first eigenvalue of one-dimensional elliptic operators with killing
Corresponding Author
Kang Dai
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, China
Correspondence
Kang Dai, School of Mathematics and Statistics, Jiangsu Normal University, 221116 Xuzhou, China.
Email: [email protected]
Search for more papers by this authorXiaobin Sun
Research Institute of Mathematical Science, Jiangsu Normal University, Xuzhou, China
Search for more papers by this authorJian Wang
School of Mathematics and Statistics, Fujian Normal University, Fuzhou, China
Key Laboratory of Analytical Mathematics and Applications (Ministry of Education), Fujian Normal University, Fuzhou, China
Fujian Provincial Key Laboratory of Statistics and Artificial Intelligence, Fujian Normal University, Fuzhou, China
Search for more papers by this authorYingchao Xie
Research Institute of Mathematical Science, Jiangsu Normal University, Xuzhou, China
Search for more papers by this authorCorresponding Author
Kang Dai
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, China
Correspondence
Kang Dai, School of Mathematics and Statistics, Jiangsu Normal University, 221116 Xuzhou, China.
Email: [email protected]
Search for more papers by this authorXiaobin Sun
Research Institute of Mathematical Science, Jiangsu Normal University, Xuzhou, China
Search for more papers by this authorJian Wang
School of Mathematics and Statistics, Fujian Normal University, Fuzhou, China
Key Laboratory of Analytical Mathematics and Applications (Ministry of Education), Fujian Normal University, Fuzhou, China
Fujian Provincial Key Laboratory of Statistics and Artificial Intelligence, Fujian Normal University, Fuzhou, China
Search for more papers by this authorYingchao Xie
Research Institute of Mathematical Science, Jiangsu Normal University, Xuzhou, China
Search for more papers by this authorAbstract
In this paper, we investigate the first eigenvalue for one-dimensional elliptic operators with killing. Two-sided approximation procedures and basic estimates of the first eigenvalue are given in both the half line and the whole line. The proofs are based on the -transform, Chen's dual variational formulas, and the split technique. In particular, a few examples are presented to illustrate the power of our results.
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