An expansion of the solution of Dirichlet boundary value problem for Berger equation

The Dirichlet boundary value problem for Berger equation is reduced to the successive sequence of boundary value problems, which may be decomposed into a coupled systems of Poisson and Helmholtz equations. Convergence of a series in solutions of the systems of coupled equations to the solution of Berger boundary value problem with Dirichlet and the mixed boundary conditions is established. The bounds for the coupling function are found and explicit value of the upper bound is obtained for the biharmonic boundary value problem in a circular domain.