Multiparameter Sturm-Liouville problems with eigenparameter dependent boundary conditions

Bhattacharyya, Tirthankar ; Binding, H. ; Seddighi, P. A. (2001) Multiparameter Sturm-Liouville problems with eigenparameter dependent boundary conditions Journal of Mathematical Analysis and Applications, 264 (2). pp. 560-576. ISSN 0022-247X

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Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1006/jmaa.2001.7695

Abstract

A system of ordinary differential equations,− y″j + qjyj = ∑k = 1nλkrjkyj, j = 1,…,n, 0.1 with real valued and continuous coefficient functions qj, rjk is studied on [0, 1] subject to boundary conditionsy′j0yj0 = cot Βj and bjyj1 − djy′j1 = eTjλcjy′j1 − ajyj1 0.2for j = 1,…,n. Here ET = [e11 e2 ··· en] is an arbitrary n × n matrix of real numbers and ωj = ajdj − bjcj ≠ 0. A point λ = [λ1 ··· λn]T ∈ Cn satisfying (0.1) and (0.2) is called an eigenvalue of the system. Results are given on the existence and location of the eigenvalues and completeness and oscillation of the eigenfunctions.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
ID Code:99507
Deposited On:27 Nov 2016 12:54
Last Modified:29 Nov 2016 09:57

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