In this paper, as far as we know, the numerical solution of the singularly perturbed boundary value problem containing both control parameter and integral condition is first being considered.
For smooth boundary-value problems containing first and second derivatives the error estimates converge to the exact error as the mesh is refined.
We construct an algebra of pseudo-differential boundary value problems that contains the classical Shapiro Lopatinskij elliptic problems as well as all differential elliptic problems of Dirac type with APS boundary conditions, together with their parametrices.
We introduce here a new algebra of boundary value problems that contains Shapiro Lopatinskij elliptic as well as global projection conditions; the latter ones are necessary, if an analogue of the Atiyah Bott obstruction does not vanish.
This monograph is directed to different kinds of boundary value problems and contains new researches on the existence, uniqueness, and multiplicity of solutions of different types of problems as -point, -laplacian, or higher-order equations together with functional and impulsive equations with singularities.
In the paper of A.N. Tikhonov [14] boundary value problems with boundary conditions containing derivatives of higher order have been investigated for the heat equation.
We want to emphasize that the boundary value problem studied here differs from standard boundary value problems in that it contains transmission conditions and the eigenvalue parameter appears not only in the differential equation, but also in the boundary conditions.
In recent years, there has been a growing interest in physical applications of boundary value problems with a spectral parameter, contained in the boundary conditions.
