Abstract: The singularly perturbed boundary value problem for a class of nonlinear nonlocal elliptic equation of higher order was considered. Under suitable conditions, the outer solution of the original problem was obtained. Then, applying the multiple scales variable and the method of component expansion, the first and second boundary layer corrective terms were constructed and the formal asymptotic expansion was obtained. Finally, applying the theory of differential inequalities the asymptotic expansion of a solution for the boundary value problem with two parameters was studied. Some relational inequalities were educed. And the existence of the solution for the original problem and the uniformly valid asymptotic estimation were discussed.

Key words: nonlocal, elliptic equation, singular perturbation