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Bull. Korean Math. Soc. 2015; 52(1): 223-238

Printed January 31, 2015

https://doi.org/10.4134/BKMS.2015.52.1.223

Copyright © The Korean Mathematical Society.

Eigenvalue inequalities of the Schr\"{o}dinger-type operator on bounded domains in strictly pseudoconvex CR manifolds

Feng Du, Yanli Li, and Jing Mao

Jingchu University of Technology, Jingchu University of Technology, Harbin Institute of Technology (Weihai)

Abstract

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In this paper, we study the eigenvalue problem of Schr\"{o}ding\-er-type operator on bounded domains in strictly pseudoconvex CR manifolds and obtain some universal inequalities for lower order eigenvalues. Moreover, we will give some generalized Reilly-type inequalities of the first nonzero eigenvalue of the sub-Laplacian on a compact strictly pseudoconvex CR manifold without boundary.

Keywords: sub-Laplacian, Schr\"{o}dinger-type operator, eigenvalues, universal inequalities, strictly pseudoconvex CR manifolds

MSC numbers: Primary 35P15, 53C42, 58G25

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