We consider Euler equations with stratified background state that is valid for internal water waves. The solution of the initial-boundary problem for Boussinesq approximation in the waveguide mode is presented in terms of the stream function. The orthogonal eigenfunctions describe a vertical shape of the internal wave modes and satisfy a Sturm-Liouville problem. The horizontal profile is define...

In formal scattering theory, Green functions are obtained as solutions of a distributional equation. In this paper, we use the Sturm-Liouville theory to compute Green functions within a rigorous mathematical theory. We shall show that both the Sturm-Liouville theory and the formal treatment yield the same Green functions. We shall also show how the analyticity of the Green functions as function...

If a Sturm-Liouville problem is given in an open interval of the real line then regular boundary value problems can be considered on compact sub-intervals. For these regular problems, all with necessarily discrete spectra, the eigenvalues depend on both the end-points of the compact intervals, and upon the choice of the real separated boundary conditions at these end-points. These eigenvalues a...

An inverse nodal problem consists in reconstructing this operator from the given zeros of their eigenfunctions. In this work, we are concerned with the inverse nodal problem of the Sturm-Liouville operator with eigenparameter dependent boundary conditions on a finite interval. We prove uniqueness theorems: a dense subset of nodal points uniquely determine the parameters of the boundary conditio...

In this paper, we present a comparative study of Sinc-Galerkin method and differential transform method to solve Sturm-Liouville eigenvalue problem. As an application, a comparison between the two methods for various celebrated Sturm-Liouville problems are analyzed for their eigenvalues and solutions. The study outlines the significant features of the two methods. The results show that these me...

In this paper, we studied q-analogue of Sturm–Liouville boundary value problem on a finite interval having discontinuity in an interior point. We proved that the q-Sturm–Liouville is self-adjoint modified Hilbert space. investigated spectral properties eigenvalues and eigenfunctions problem. shown are form complete system. Finally, sampling theorem for integral transforms whose kernels basic fu...

The objective of the current study is to develop a simple formula to estimate the fundamental vibration period of tall buildings for using in equivalent lateral force analysis specified in building codes. The method based on Sturm-Liouville differential equation is presented here for estimating the fundamental period of natural vibration. The resulting equation, based on the continuum represent...

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.