On nonlocal problems for ordinary differential equations and on a nonlocal parabolic transmission problem.
On Orthogonal Series Solution For Boundary Layer Problems
On periodic-type solutions of systems of linear ordinary differential equations.
On Poisson-Dirichlet problems with polynomial data
In this note we provide a probabilistic proof that Poisson and/or Dirichlet problems in an ellipsoid in Rd, that have polynomial data, also have polynomial solutions. Our proofs use basic stochastic calculus. The existing proofs are based on famous lemma by E. Fisher which we do not use, and present a simple martingale proof of it as well.
On relation between stability and correctness of linear systems of generalized ordinary differential equations.
On some boundary value problems for ordinary linear differential equations of second order in the Colombeau algebra
On Some Difference Schemes for Singular Singularly-Perturbed Boundary Value Problems.
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 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 comparison of error bounds for finite difference schemes.
On the correctness of linear 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 existence of nonnegative solutions of the periodic boundary value problem for a system of linear generalized ordinary differential equations.
On the existence of solutions for a class of first-order differential equations.
On the generalized boundary value problem
In the paper it is proved that the generalized linear boundary value problem generates a Fredholm operator. Its index depends on the number of boundary conditions. The existence results of Landesman-Lazer type are given as an application to nonlinear problems by using dual generalized boundary value problems.
On the isospectral beams.
On the necessary and sufficient conditions for the convergence of the difference schemes for the general boundary value problem for the linear systems of ordinary differential equations
We consider the numerical solvability of the general linear boundary value problem for the systems of linear ordinary differential equations. Along with the continuous boundary value problem we consider the sequence of the general discrete boundary value problems, i.e. the corresponding general difference schemes. We establish the effective necessary and sufficient (and effective sufficient) conditions for the convergence of the schemes. Moreover, we consider the stability of the solutions of general...
On the Number of Solutions of the Equation ...= ...aj(t)xj, 0...t...1, for which x(0) = x(1).
On the Optimum Choice of Weight Functions in a Class of Variational Calculations.
On the question of solvability of a periodic boundary value problem for a system of linear generalized ordinary differential equations.