Coupling constant limits of Schrödinger operators with critical potentials
1 Mathematics and Statistics School, Henan University of Science and Technology, No. 263, Luo-Long District, Kai-Yuan Road, Luoyang City, Henan Province, 471023, China
2 College of Civil Engineering and Architecture, Zhejiang University, B505 Anzhong Building, 866 Yuhangtang Road, Hangzhou, Zhejiang Province, 310058, China
Boundary Value Problems 2013, 2013:62 doi:10.1186/1687-2770-2013-62Published: 27 March 2013
A family of Schrödinger operators, , is studied in this paper. Here with when is large enough and for some . We show that each discrete eigenvalue of tends to 0 when λ tends to some . We get asymptotic behavior of the smallest discrete eigenvalue when λ tends to .