Dependence of eigenvalues of Sturm– Liouville problems with interface conditions

Eigenvalues of regular fourth‐order Sturm–Liouville problems with transmission conditions

“…However, this does not mean for a fixed n , the n ‐th eigenvalue λ n ( ω ) is always continuous in ω . See Remark 1 in .…”

“…In this paper, we generalize the results of [5] in fourth-order case, according to the classification of general boundary conditions [17]; we consider a regular fourth-order Sturm-Liouville problem with separated conditions, coupled conditions and transmission conditions, and show that the eigenvalues of the problems are differentiable functions of all the data: the end point, the boundary conditions, transmission conditions as well as the coefficients and the weight function and find expressions for their derivatives.…”

“…Such problems are connected with discontinuous material properties, such as heat and mass transfer [1], vibrating string problems when the string loaded additionally with point masses and diffraction problems. To deal with interior discontinuities, some conditions are imposed on the discontinuous points, which are often called transmission conditions, interface conditions or point interactions [2][3][4][5][6][7][8]. The various physics applications of this kind of problems are found in many literatures, here we mention the results of [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] and corresponding references cited therein.…”

“…For fourth‐order case, Suo and Wang in consider eigenvalues of a class of regular fourth‐order Sturm–Liouville problems and obtain similar results for the eigenvalues, the numerical computation of the eigenvalues and eigenfunctions of Sturm–Liouville problems is SLEUTH . In a recent paper, Zhang and Wang in consider the dependence of eigenvalues of Sturm–Liouville problems with interface conditions for second‐order case and give the differential expressions of eigenvalues with respect to the boundary conditions, interface conditions as well as the coefficients and the weight function.…”

A discontinuous Sturm–Liouville problem with boundary conditions rationally dependent on the eigenparameter

“…To deal with interior discontinuities, some conditions, which are often called transmission conditions [10][11][12][13], interface conditions [14,16], are imposed on the discontinuous points. Mukhtarov et al in [13] considered eigenparameter dependent Sturm-Liouville problems with transmission conditions and obtained some properties of eigenvalues.…”