Partial difference equations arising in numerical schemes and game theory

摘要

A functional analytic method is used to prove that some linear and non-linear partial difference equations of two, three and four variables, which arise in numerical schemes and game theory, have a unique solution in the spaces l2N2 or l1N2,l1N3 and l1N4, respectively. In the case of non-linear difference equations a region, which depends on the initial conditions and the parameters of the equation, where the solution holds, is given. For both linear and non-linear difference equations a bound of the solution is determined.