Recently, there appeared a considerable interest in inverse Sturm–Liouville-type problems with constant delay. However, necessary and sufficient conditions for solvability of such were obtained only one very particular situation. Here we address this gap by obtaining the case functional-differential pencils possessing more general form along nonlinear dependence on spectral parameter. For purpo...

In this paper, we consider the negative order Korteweg–de Vries equation with a self-consistent integral source. It is shown that negative-order source can be integrated by method of inverse spectral problem. The evolution data Sturm–Liouville operator periodic potential associated solution determined. obtained results make it possible to apply problem solve in class functions.

This paper deals with the boundary value problem involving the differential equation ell y:=-y''+qy=lambda y, subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions y(d+0)=a y(d-0), y'(d+0)=ay'(d-0)+b y(d-0). In this problem q(x), d, a , b are real, qin L^2(0,pi), din(0,pi) and lambda is a parameter independent of x. By defining a new...

We give an example of an indefinite weight Sturm-Liouville problem whose eigenfunctions form a Riesz basis under Dirichlet boundary conditions but not under anti-periodic boundary conditions.

In this study, we establish a Parseval equality and an expansion formula for a Sturm– Liouville operator on semi-unbounded time scales. AMS subject classification: 34L10.

We solve the inverse spectral problem for a class of Sturm–Liouville operators with singular nonlocal potentials and nonlocal boundary conditions.

We extend a result of Stolz and Weidmann on the approximation of isolated eigenvalues of singular Sturm–Liouville and Dirac operators by the eigenvalues of regular operators.