ESTIMATES OF SOLUTIONS OF THE THIRD BOUNDARY VALUE PROBLEMS FOR LINEAR DIFFERENTIAL EQUATIONS OF SECOND ORDER
Study on the solvability nonclassical boundary value problems for ordinary differential equations of the second order and the development of numerical methods for solving them makes it necessary to obtain estimates of solutions of local boundary value problems for these equations.A similar problem arises in the solution of boundary value problems for loaded differential equations in differential and finite-difference formulations.This work is devoted to the third boundary value problem for the Sturm-Liouville. Under certain conditions, the input data of the problem is obtained pointwise estimate of the solution. The paper also received a priori estimate of the solution of the problem in the uniform metric, which enhances the well-known uniform estimate.The results obtained using the representation of the solution of the problem with the help of Green´s functions and known differential inequalities, in particular, comparison theorem Sturm.