An inverse nodal problem for differential pencils with complex spectral parameter dependent boundary conditions

Abstract

Abstract:In this study, we are concerned with an inverse nodal problem for second order differential pencil on a finite interval with complex spectral parameter dependent boundary conditions by using nodal points. We give some reconstruction formulas for potential functions p and q as a limit.

On recovering quadratic pencils with singular coefficients and entire functions in the boundary conditions

“…At the present time, there are no works for quadratic pencils with entire functions of general form in the boundary conditions. For the cases of linear and polynomial dependence on the spectral parameter, results in inverse problems were obtained in [22][23][24][25][26].…”

On the spectral properties of a Sturm-Liouville problem with eigenparameter in the boundary condition

“…Sturm-Liouville problems with the boundary conditions depending on the spectral parameter were studied in order to investigate their various properties in many articles (see [1,2,[6][7][8][10][11][12][13][14][15][16][17][19][20][21][22][23]25]). The problems on the basis property of system of root functions corresponding to Sturm-Liouville problems for some differential operators which contain different forms (linearly, rationally, quadratically etc.)…”