Systems of equations: particular examples

Abstract

No general theory for systems of nonlinear equations exists. Systems usually require a combination of specific, sometimes very sophisticated tricks, possibly with a fixed-point technique finely fitted to a particular structure. Although certain general approaches can be adopted,1 a pragmatic observation is that systems are much more difficult than single equations and sometimes only partial results (typically for small data) can be obtained with current knowledge. Even worse, many natural systems arising from physical problems still remain unsolved with respect to even the existence of a solution; in particular cases, however, this may be related with an oscillatory-like or explosion-like character of related evolutionary systems which thus lack any steady states that would solve these stationary systems.