The Sturm-Liouville problem with a nonlocal boundary condition

On The Stability Of Finite-Difference Schemes For Parabolic Equations Subject To Integral Conditions With Applications To Thermoelasticity

“…This effect is not present at all provided h is sufficiently small, i.e., h < h 1 = 0.1. This holds for the poles of the characteristic function (for more detail see [18]). …”

A survey on stationary problems, Green's functions and spectrum of Sturm–Liouville problem with nonlocal boundary conditions

“…The analysis of stationary problem with one classical boundary condition (γ 0 = 0) and another NBC [197,214,218] and investigation of auxiliary stationary problems [107,187,198] shows that restrictions γ 0 0 and γ 1 0 are not necessary, and, in general case, we can take γ 0 , γ 1 ∈ R. The main research tools in [35,36] were the maximum principle and comparison theorems. Existence and uniqueness of a solution for the stationary problem is equivalent to existence of zero eigenvalue.…”

“…More results about real eigenvalues for this problem are in [214]. SLP (40)- (41) with one of the two cases of integral type NBCs…”

On the stability of a weighted finite difference scheme for wave equation with nonlocal boundary conditions

“…The spectrum and characteristic functions for eigenvalues of Sturm-Liouville problem are widely investigated in [9][10][11][12]. For example, the following problemś…”