On solution of an ill-posed problem for a semilinear differential equation

An extensive literature is devoted to the ill-posed problems connected with a nonlinear operator and differential-operator equations. A regularization method is usually constructed by using the “operator” approach and special properties of the problem operator (for instance, monotonicity). In this paper, stable approximate solutions of an ill-posed differential problem are constructed by a method of the quasi-inversion type. The convergence of the constructed approximate solutions to the exact solution of the initial problem is investigated.