in this paper, we investigate a singular perturbation problem including a fourth order o.d.e. with general linear boundary conditions. firstly, we obtain the necessary conditions of solution of o.d.e. by making use of fundamental solution, then by compatibility of these conditions with boundary conditions, we determine that, for given perturbation problem, whether boundary layer is formed or not.

we investigate the boundary-value problem generated by the sturm-liouville equation withdiscontinuous coefficients, eigenparameter dependent boundary conditions and transmission conditionsat the point of discontinuity. with a different approach we introduce an adequate hilbert spaceformulation, investigate some properties of eigenvalues, green’s function and resolvent operator, andfind simple c...

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...

this paper presents the bending analysis of annular plates by the indirect trefftz boundary approach. the formulation for thin and thick plates is based on the kirchhoff plate theory and the reissner plate theory. the governing equations are therefore a fourth-order boundary value problem and a sixth-order boundary value problem, respectively. the trefftz method employs the complete set of solu...

‎In the present paper‎, ‎some spectral properties of boundary value problems of Sturm-Liouville type on two disjoint bounded intervals with transmission boundary conditions are investigated‎. ‎Uniqueness theorems for the solution of the inverse problem are proved‎, ‎then we study the reconstructing of the coefficients of the Sturm-Liouville problem by the spectrtal mappings method.

height is amongst the most delicate subjects of geodesy. thanks to the global navigation satellite systems (gnss) like gps or glonass, 3d point positioning of points, by geometrical positioning, since years ago has become a common practice. the height derived from these ways has a geometrical concept. in civil projects the physical concept of the height is more demanded. orthometric height, , i...

This paper presents the bending analysis of annular plates by the indirect Trefftz boundary approach. The formulation for thin and thick plates is based on the Kirchhoff plate theory and the Reissner plate theory. The governing equations are therefore a fourth-order boundary value problem and a sixth-order boundary value problem, respectively. The Trefftz method employs the complete set of solu...

The BEM is applied to the solution of the torsion problem of non-homogeneous anisotropic non-circular prismatic bars. The problem is formulated in terms of the warping function. This formulation leads to a second order partial differential equation with variable coefficients, subjected to a generalized Neumann type boundary condition. The problem is solved using the Analog Equation Method (AEM)...

krein [1] mentioned that for each pd equation we have two extreme operators, one is the minimal in which solution and its derivatives on the boundary are zero, the other one is the maximal operator in which there is no prescribed boundary conditions. they claim it is not possible to have a related boundary value problem for an arbitrarily chosen operator in between. they have only considered lo...

this paper considers a class of one-dimensional solidification problem in which kinetic undercooling is incorporated into the temperature condition at the interface. a model problem with nonlinear kinetic law is considered. the main result is an existence theorem. the mathematical effects of the kinetic term are discussed