Two-parameter uniformly elliptic Sturm–Liouville problems with eigenparameter-dependent boundary conditions

Bhattacharyya, Tirthankar ; Mohandas, J. P. (2005) Two-parameter uniformly elliptic Sturm–Liouville problems with eigenparameter-dependent boundary conditions Proceedings of the Edinburgh Mathematical Society, 48 (3). pp. 531-547. ISSN 0013-0915

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Official URL: https://www.cambridge.org/core/journals/proceeding...

Related URL: http://dx.doi.org/10.1017/S0013091504000720

Abstract

We consider the two-parameter Sturm–Liouville system –y "1+q1y1=(λr11+μr12)y1 [0,1], with the boundary conditions y'1(0)/y1(0)=cotΑ1 and y'1(1)/y1(1)=a1λ+b1/c1λ+d1 and –y" 2+q2y2=(λr21+μr22)y2 on [0,1] with the boundary conditions y'2(0)/y2(0)=cotΑ2 and y'2(1)/y2(1)=a2μ+b2/c2μ+d2 subject to the uniform-left-definite and uniform-ellipticity conditions; where and qi and rij are continuous real valued functions on [0,1], the angle Αi is in [0, π) and ai, bi, ci, di, and are real numbers with δ i = aidi - bici > 0 and ci ≠0 for i,j = 1,2. Results are given on asymptotics, oscillation of eigenfunctions and location of eigenvalues.

Item Type:Article
Source:Copyright of this article belongs to Edinburgh Mathematical Society.
Keywords:Sturm–Liouville Equations; Definiteness Conditions; Eigencurves; Oscillation Theorems
ID Code:99874
Deposited On:27 Nov 2016 12:50
Last Modified:29 Nov 2016 06:31

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