RIGHT-DEFINITE MULTIPARAMETER STURM–LIOUVILLE PROBLEMS WITH EIGENPARAMETER-DEPENDENT BOUNDARY CONDITIONS

• Published in: Proceedings of the Edinburgh Mathematical Society Vol. 45; no. 3; pp. 565 - 578
• Main Authors: Bhattacharyya, Tirthankar, Ko$\breve{s}$ir, Toma$\breve{z}$, Plestenjak, Bor
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.10.2002
• Subjects: eigenparameter-dependent boundary conditions; eigenvalues; Minkowski definiteness conditions; multiparameter Sturm–Liouville boundary-value problems; oscillation counts; Minkowski definiteness conditions; multiparameter Sturm–Liouville boundary-value problems; eigenvalues; eigenparameter-dependent boundary conditions; oscillation counts
• ISSN: 0013-0915; 1464-3839
• DOI: 10.1017/S0013091501000207

We study a system of ordinary differential equations linked by parameters and subject to boundary conditions depending on parameters. We assume certain definiteness conditions on the coefficient functions and on the boundary conditions that yield, in the corresponding abstract setting, a right-definite case. We give results on location of the eigenvalues and oscillation of the eigenfunctions. AMS 2000 Mathematics subject classification: Primary 34B08; 34B24