Spectrum curves for a discrete Sturm–Liouville problem with one integral boundary condition - Bingelė, Kristina; Bankauskienė, Agnė; Štikonas, Artūras (Nonlinear Analysis: Modelling and Control, 2019)
This paper presents new results on the spectrum on complex plane for discrete Sturm–Liouville problem with one integral type nonlocal boundary condition depending on three parameters: γ, ξ1 and ξ2. The integral condition is approximated by the trapezoidal rule. The dependence on parameter γ is investigated by using characteristic function method and analysing spectrum curves which gives qualitative view of the spectrum for fixed ξ1 = m1 / n and ξ2 = m2 / n, where n is discretisation parameter. Some properties of the spectrum curves are formulated and illustrated in figures for various ξ1 and ξ2. *The research was partially supported by the Research Council of Lithuania (grant No. MIP-047/2014).