Spectrum Curves for Sturm–Liouville Problem with Integral Boundary Condition

• Main Authors: Agnė Skučaitė, Artūras Štikonas
• Format: Article
• Language: English
• Published: Vilnius Gediminas Technical University 2015-11-01
• Series: Mathematical Modelling and Analysis
• Subjects: Sturm–Liouville problem; characteristic function; spectrum curves; critical point; integral boundary condition
• Online Access: https://journals.vgtu.lt/index.php/MMA/article/view/1036

We consider Sturm–Liouville problem with one integral type nonlocal boundary condition depending on three parameters γ (multiplier in nonlocal condition), ξ1, ξ2 ([ξ1, ξ2] 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 ξ1, ξ2 are investigated. We present the results of modelling and computational analysis and illustrate those results with graphs.