Asymptotic solution of singular perturbation problems for the fourth-order elliptic differential equations

In this paper we consider the singularly pertubed boundary value problem for the fourth-order elliptic differential equation, establish the energy estimates of the solutionand its derivatives and construct the formal asymptotic solution by Lyuternik-Vishik's method. Finally, by means of the energy estimates we obtain the bound of the remainder of the asymptotic solution.