ABSTRACT
Nonlinear problems tend to be dealt with on an individual basis since the governing equations frequently have special features which exert a particularly dominating influence on the solutions. Nevertheless, the basic requirements are the same for all problems be they linear or nonlinear; we need information about the existence and uniqueness of solution. Once this is available we can then investigate other aspects of the solution such as their regularity and their asymptotic behaviour; in particular we can develop scattering theories. In the literature these various aspects are often treated separately for each particular problem. However, it turns out that many nonlinear problems in the applied sciences present certain common problems in abstract functional analysis. Indeed using standard linear functional analysis together with the Contraction Mapping Principle considerable progress can be made in the study of these nonlinear problems. The abstract approach can offer a unified approach and provide a means of clarifying those properties of the solution which are general and those which are dependent on the special features of the equation being considered.
