Integral bvp for singularly perturbed system of differential equations.

The article presents a two-point integral BVP for singularly perturbed systems of linear ordinary differential equations. The integral BVP for singularly perturbed systems of ordinary differential equations previously has not been considered. The paper shows the influence of nonlocal boundary conditions on the asymptotic of the solution of the regarded BVP and the significant effect of integral terms in the definition of the limiting BVP. An explicit constructive formula for the solution of this BVP using initial and boundary functions of the homogeneous perturbed equation is obtained. A theorem on asymptotic estimates of the solution and its derivatives is given. It is established that the solution of the integral BVP at the point t = 0 is infinitely large as µ → 0. From here, it follows that the solution of the considered boundary value problem has an initial jump of zero order. It is found that the solution of the original integral BVP is not close to the solution of the usual limiting unperturbed BVP. A changed limiting BVP is obtained. The presence of integrals in the boundary conditions leads to the fact that the limiting BVP is determined by the changed boundary conditions. This follows from the presence of the jump and its order. A theorem on the close between the solutions of the original perturbed and changed limiting problems is given. [ABSTRACT FROM AUTHOR]