On some two-point boundary value problems for two-dimensional systems of ordinary differential equations.
On spectral problems of discrete Schrödinger operators
A special type of Jacobi matrices, discrete Schrödinger operators, is found to play an important role in quantum physics. In this paper, we show that given the spectrum of a discrete Schrödinger operator and the spectrum of the operator obtained by deleting the first row and the first column of it can determine the discrete Schrödinger operator uniquely, even though one eigenvalue of the latter is missing. Moreover, we find the forms of the discrete Schrödinger operators when their smallest and...
On the absolutely continuous spectrum of perturbed periodic Sturm-Liouville operators.
On the approximate solution of integro-differential equations arising in oscillating magnetic fields
In this work, we propose the Shannon wavelets approximation for the numerical solution of a class of integro-differential equations which describe the charged particle motion for certain configurations of oscillating magnetic fields. We show that using the Galerkin method and the connection coefficients of the Shannon wavelets, the problem is transformed to an infinite algebraic system, which can be solved by fixing a finite scale of approximation. The error analysis of the method is also investigated....
On the basis properties of a spectral problem with a spectral parameter in a boundary condition.
On the boundary conditions associated with second-order linear homogeneous differential equations
The ideas of the present paper have originated from the observation that all solutions of the linear homogeneous differential equation (DE) satisfy the non-trivial linear homogeneous boundary conditions (BCs) , . Such a BC is referred to as a natural BC (NBC) with respect to the given DE, considered on the interval . This observation suggests the following queries : (i) Will each second-order linear homogeneous DE possess a natural BC ? (ii) How many linearly independent natural BCs can a...
On the boundedness of solutions of nonlinear second-order differential equations with parameter
On the comparison of error bounds for finite difference schemes.
On the completeness of eigenfunctions and associated functions of irregular multipoint eigenvalue-problems.
On the concave solutions of the Blasius equation.
On the convergence of multistep methods for nonlinear two-point boundary value problems
On the correct solvability of the boundary-value problem for one class operator-differential equations of the fourth order with complex characteristics.
On the correctness of linear boundary value problems for systems of generalized ordinary differential equations.
On the correctness of nonlinear boundary value problems for systems of generalized ordinary differential equations.
On the correctness of the Cauchy problem for a linear differential system on an infinite interval.
On the coupling of elliptic and hyperbolic nonlinear differential equations
On the Darboux transformation. I.
On the direction of pitchfork bifurcation.
On the discreteness of the spectra of the Dirichlet and Neumann -biharmonic problems.
On the domain of selfadjoint extension of the product of Sturm-Liouville differential operators.