Анализ свойств решений краевых задач для диф- ференциальных уравнений высоких порядков

The relativistic generalization of potential model of a quarkonium leads to the solution of a spectroscopic problem for quasipotential equations. In that specific case the problem is reduced to the investigation of a boundary problem for the ordinary differential equation of the terminating order with arbitrary parameter at the higher derivatives. In the work the algorithm of investigation of boundary problems for the differential equations of high orders is offered. The algorithm is realized with the use of system of symbolical evaluations MAPLE. It is erected, that at → 0 some solutions coincide with the solution of the nonrelativistic Schrodinger equation. Besides, are found out, so-called frontier layer solutions; transition of one type of the solution (for example, the solution with one junction) in to another (the solution without junctions). Investigations of properties of eigenvalues and eigenfunctions are carried out at various values of.