Probabilistic Analysis of Semilinear Partial Differential Equations

摘要

A major thrust of the original proposal was to find new probabilistic methods for dealing with semilinear partial differential equations. Mathematicians are currently devoting more of their attention to studying nonlinear partial differential equations since they recognize that descriptions of physical phenomena must incorporate nonlinear behavior. The author succeeded in finding a method for solving systems of semilinear elliptic equations by a new procedure which does not need the old hypotheses of quasi-monotone systems. It combines probability, analysis and a transfinite induction scheme to solve equations of a certain on a domain E in R sub d subject to boundary conditions u sub 1 = u sub 2 = ... u sub n 0 on the boundary of E. (kr)