An approach to solving an ill-posed problem for a nonlinear differential equation

A reverse time problem is considered for a semilinear differential equation. We suggest an approach to construct approximate solving methods for the problem under study. The approach generalizes the scheme proposed by A. B. Bakushinskii for linear ill-posed problems. Two-sided error estimates for the proposed methods are obtained via the error estimates for the corresponding linear problem on standard correctness classes. Order optimality is proved for the considered algorithms.