The first eigenvalue of one‐dimensional elliptic operators with killing

Kang Dai, Xiaobin Sun, Jian Wang and Yingchao Xie

Mathematische Nachrichten, 2025, vol. 298, issue 1, 282-311

Abstract: 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 h$h$‐transform, Chen's dual variational formulas, and the split technique. In particular, a few examples are presented to illustrate the power of our results.

Date: 2025
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https://doi.org/10.1002/mana.202400331

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