On a class of non-self-adjoint periodic eigenproblems with boundary and interior singularities

[摘要] We prove that all the eigenvalues of a certain highly non-self-adjoint Sturm-Liouville differential operator are real. The results presented are motivated by and extend those recently found by various authors (Benilov et al. (2003) [3], Davies (2007) [7] and Weir (2008) [18]) on the stability of a model describing small oscillations of a thin layer of fluid inside a rotating cylinder. (C) 2010 Elsevier Inc. All rights reserved.

[发布日期] 2010-12-15

[关键词] Non-Hermitian Hamiltonians;PT-symmetry;Non-self-adjoint;Sturm-Liouville operators