A nonlinear model involving M-operators. An amplification effect measured in the cascade of vision

An amplification effect measured in the cascade of vision forms a basis to formulate an abstract nonlinear model offering a generalization of the cascade problem. This model is analyzed and some conditions concerning the existence and/or possible uniqueness and multiplicity of solutions are presented. An essential feature of the model is that the appropriate operators governing the problem are not surjective. For the case of unique solvability a numerical procedure is proposed and its convergence is proved.