On the convergence of the method of reduction to ordinary differential equations

In my previous paper [1], sufficient conditions for convergence of a min­ imizing sequence to a solution of a partial differential equation were given. It was shown there that, for convergence of a minimizing sequence, it is important for the expression en — I(un) — I{u) = I x{un — u) to diminish rapidly enough. In this paper, considering our method of reduction to ordi­ nary differential equations proposed in [2], we find conditions under which we are sure that en diminishes with sufficient rate.