Dependence of Eigenvalues of a Class of Higher-Order Sturm-Liouville Problems on the Boundary. (3rd March 2015)

• Record Type: Journal Article
• Authors: Yang, Qiuxia; Wang, Wanyi; Gao, Xingchao
• Other Names: Rajendran Sellakkutti Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2015(2015)
• Publication Date: 2015-03-03
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2015/686102
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : We show that the eigenvalues of a class of higher-order Sturm-Liouville problems depend not only continuously but also smoothly on boundary points and that the derivative of then th eigenvalue as a function of an endpoint satisfies a first order differential equation. In addition, we prove that as the length of the interval shrinks to zero all2k th-order Dirichlet eigenvalues march off to plus infinity; this is also true for the first (i.e., lowest) eigenvalue.