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

Boulton, L., Levitin, M. ORCID: https://orcid.org/0000-0003-0020-3265 and Marletta, M. (2010) On a class of non-self-adjoint periodic eigenproblems with boundary and interior singularities. Journal of Differential Equations, 249 (12). pp. 3081-3098. ISSN 0022-0396 doi: 10.1016/j.jde.2010.08.010

Abstract/Summary

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.