Belinskiy, B. P.; Dauer, J. P. On a regular Sturm-Liouville problem on a finite interval with the eigenvalue parameter appearing linearly in the boundary conditions. (English) Zbl 0879.34035 Hinton, Don (ed.) et al., Spectral theory and computational methods of Sturm-Liouville problems. Proceedings of the 1996 conference, Knoxville, TN, USA, in conjunction with the 26th Barrett memorial lecture series. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 191, 183-196 (1997). This work is devoted to a regular Sturm-Liouville problem on a finite interval with the eigenvalue parameter appearing linearly in the boundary conditions. Its eigenfunctions are to be understood in the sense of Sobolev. The authors reduce this problem to an operator pencil (polynomial) equation in some Hilbert space. It is shown that the eigenfunctions for this class of problems form a Riesz basis. Some properties of eigenvalues are presented. In particular, lower bound estimation for eigenvalues is obtained.For the entire collection see [Zbl 0866.00046]. Reviewer: S.Yanchuk (Kiev) Cited in 8 Documents MSC: 34B24 Sturm-Liouville theory Keywords:Sturm-Liouville problem; generalized solution; operator pencil; Riesz basis PDFBibTeX XMLCite \textit{B. P. Belinskiy} and \textit{J. P. Dauer}, Lect. Notes Pure Appl. Math. 191, 183--196 (1997; Zbl 0879.34035)