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A nonlocal problem for loaded partial differential equations of fourth order A nonlocal problem for the fourth order system of loaded partial differential equations is considered. The questions of a existence unique solution of the considered problem and ways of its construction are investigated. The nonlocal problem for the loaded partial differential equation of fourth order is reduced to a nonlocal problem for a system of loaded hyperbolic equations of second order with integral conditions by introducing new functions. As a result of solving nonlocal problem with integral conditions is applied a method of introduction functional parameters. The algorithms of finding the approximate solution to the nonlocal problem with integral conditions for the system of loaded hyperbolic equations are proposed and their convergence is proved. The conditions of the unique solvability of the nonlocal problem for the loaded hyperbolic equations are obtained in the terms of initial data. The results also formulated relative to the original problem.

On the unique solvability of a family of multipoint-integral boundary value problems for a third order differential equation A family multipoint-integral boundary value problems for a third order differential equation with variable coefficients is considered. The questions of a existence unique solution of the considered problem and ways of its construction are investigated. The family multipoint-integral boundary value problems for the differential equation of third order with variable coefficients is reduced to a family multipoint-integral boundary value problems for a system of three differential equations by introducing new functions. For solve of resulting family of multipoint-integral boundary value problems is applied a parametrization method. An algorithms of finding the approximate solution to the family multipoint-integral boundary value problems for the system of three differential equations are proposed and their convergence is proved. The conditions of the unique solvability of the family multipoint-integral boundary value problems for the system of three differential equations are obtained in the terms of initial data. The results also formulated relative to the original of the family multipoint-integral boundary value problems for the differential equation of third order with variable coefficients.

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