Spectrum Curves for Sturm-Liouville Problem with Integral Boundary Condition

• Published in: Mathematical modelling and analysis Vol. 20; no. 6; pp. 802 - 818
• Main Authors: Skucaite, Agne, Stikonas, Arturas
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 02.11.2015; Vilnius Gediminas Technical University
• Subjects: Boundary value problems; characteristic function; critical point; Curves (Geometry); integral boundary condition; Mathematical research; spectrum curves; Sturm-Liouville problem; integral boundary condition; critical point; spectrum curves; Sturm–Liouville problem; characteristic function
• ISSN: 1392-6292; 1648-3510; 1648-3510
• DOI: 10.3846/13926292.2015.1116470

We consider Sturm-Liouville problem with one integral type nonlocal boundary condition depending on three parameters γ (multiplier in nonlocal condition), ξ 1 , ξ 2 ([ξ 1 , ξ 2 ] is a domain of integration). The distribution of zeroes, poles, and constant eigenvalue points of Complex Characteristic Function is presented. We investigate how Spectrum Curves depend on the parameters of nonlocal boundary conditions. In this paper we describe the behaviour of Spectrum Curves and classify critical points of Complex-Real Characteristic function. Phase Trajectories of critical points in Phase Space of the parameters ξ 1 , ξ 2 are investigated. We present the results of modelling and computational analysis and illustrate those results with graphs.