Spectrum Curves for Sturm–Liouville Problem with Integral Boundary Condition

* The research was partially supported by the Research Council of Lithuania (grant No. MIP-047/2014).

Abstract

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.

Keywords:

• Sturm–Liouville problem
• characteristic function
• spectrum curves
• critical point
• integral boundary condition

AMS Subject Classification:

• 34B24
• 34B09
• 34B15

Notes

* The research was partially supported by the Research Council of Lithuania (grant No. MIP-047/2014).