Related papers: Essentially isospectral transformations and their …
We examine the spectrum of a family of Sturm--Liouville operators with regularly spaced delta function potentials parametrized by increasing strength. The limiting behavior of the eigenvalues under this spectral flow was described in a…
It is natural to consider continuous dependence of the $n$-th eigenvalue on $d$-dimensional ($d\geq2$) Sturm-Liouville problems after the results on $1$-dimensional case by Kong, Wu and Zettl [14]. In this paper, we find all the boundary…
In this paper, we consider a problem for the first order Dirac differential equations system with spectral parameter dependent in boundary condition. The asymptotic behaviors of eigenvalues, eigenfunctions and normalizing numbers of this…
In this paper we study spectral properties of Dirichlet-to-Neumann map on differential forms obtained by a slight modification of the definition due to Belishev and Sharafutdinov. The resulting operator $\Lambda$ is shown to be self-adjoint…
In H\"ormander inner product spaces, we investigate initial-boundary value problems for an arbitrary second order parabolic partial differential equation and the Dirichlet or a general first-order boundary conditions. We prove that the…
We study a Dirichlet-to-Neumann eigenvalue problem for differential forms on a compact Riemannian manifold with smooth boundary. This problem is a natural generalization of the classical Steklov problem on functions. We derive a number of…
We consider spectral problems for the Sturm-Liouville operator with arbitrary complex-valued potential q(x) and degenerate boundary conditions. We solve corresponding inverse problem, and also study the completeness property and the basis…
All Darboux integrable difference equations on the quad-graph are described in the case of the equations that possess autonomous first-order integrals in one of the characteristics. A generalization of the discrete Liouville equation is…
The inverse problem for the Sturm- Liouville operator with complex periodic potential and discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the operator is…
We consider two main inverse Sturm-Liouville problems: the problem of recovery of the potential and the boundary conditions from two spectra or from a spectral density function. A simple method for practical solution of such problems is…
In this paper we establish new renormalized oscillation theorems for discrete symplectic eigenvalue problems with Dirichlet boundary conditions. These theorems present the number of finite eigenvalues of the problem in arbitrary interval…
In this study, we are concerned with spectral problems of second-order vector dynamic equations with two-point boundary value conditions and mixed derivatives, where the matrix-valued coefficient of the leading term may be singular, and the…
We study the eigenvalue problem for the Dirichlet Laplacian in bounded simply connected plane domains $\Omega\subset\mathbb{C}$ using conformal transformations of the original problem to the weighted eigenvalue problem for the Dirichlet…
In this paper, we for the first time get constructive solution for the inverse Sturm-Liouville problem with complex-valued singular potential and with polynomials of the spectral parameter in the boundary conditions. The uniqueness of…
The Darboux-Dressing Transformations are applied to the Lax pair associated to systems of coupled nonlinear wave equations in the case of boundary values which are appropriate to both bright and dark soliton solutions. The general formalism…
The fractional Sturm-Liouville eigenvalue problem appears in many situations, e.g., while solving anomalous diffusion equations coming from physical and engineering applications. Therefore to obtain solutions or approximation of solutions…
The main issues of the spectral theory of Dirac operators are presented, namely: transformation operators, asymptotics of eigenvalues and eigenfunctions, description of symmetric and self-adjoint operators in Hilbert space, expansion in…
We study various direct and inverse spectral problems for the one-dimensional Schr\"{o}dinger equation with distributional potential and boundary conditions containing the eigenvalue parameter.
We study Darboux transformations associated with the focusing nonlinear Schr\"odinger equation (NLS_-) and their effect on spectral properties of the underlying Lax operator. The latter is a formally J-self-adjoint (but non-self-adjoint)…
We consider the spectral problem for the Grushin Laplacian subject to homogeneous Dirichlet boundary conditions on a bounded open subset of $\mathbb{R}^N$. We prove that the symmetric functions of the eigenvalues depend real analytically…