Singular problem with boundary conditions

Solutions of nonlinear singularly perturbed differential equations with boundary conditions are studied in this work. Here the stability conditions are satisfied. We choose a starting point, but this is a boundary value problem. The peculiarity and novelty of this work lies in the fact that here the considered boundary conditions. The method of successive approximations is used to prove the existence of solutions. We also use the majorant method to prove the convergence of solutions. To prove the uniqueness of solutions, we use the contradiction method. The solution of the stated problem is considered in the real area. Using the features of the nonlinear problem, we expand the function in a Taylor series. Therefore, we bring the problem to a new form. This is another problem that can be solved in the real area. As a result, the asymptotic closeness of the solution of the perturbed and unperturbed problems is proved.