Abstract
In this paper the Sturm-Liouville problem with one classical and the other nonlocal two-point or integral boundary condition is investigated. Critical points of the characteristic function are analyzed. We investigate how distribution of the critical points depends on nonlocal boundary condition parameters. In the first part of this paper we investigate the case of negative critical points.
Highlights
Differential problems with nonlocal boundary conditions arise in various fields of biology, biotechnology, physics, etc
The analysis of eigenvalues of the difference operator with a nonlocal condition permits us to investigate the stability of difference schemes and corroborate the convergence of iterative methods [1,2,3,4,5] and it is of interest in itself
Investigation of the spectra of differential equations with nonlocal conditions is quite a new area related to the problems of this type
Summary
Differential problems with nonlocal boundary conditions arise in various fields of biology, biotechnology, physics, etc. Eigenvalues and eigenfunctions of differential problems with nonlocal two-point boundary conditions are investigated by A.V. Gulin and V. Peciulyte [10,11,12,13] Such problems with nonlocal integral boundary conditions are analyzed B. Investigation of the spectra of differential equations with nonlocal conditions is quite a new area related to the problems of this type. For the fixed parameter ξ, dependence of spectra of these problems on the parameter γ in nonlocal boundary conditions has been investigated in the previous research (see, [8, 11, 13, 15, 17]) and S. We extend here our investigation and the new results on the critical points of the characteristic functions are presented.
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