Existence of a maximal solution for quasimonotone elliptic systems
Enzo Mitidieri, Guido H. Sweers · Differential and Integral Equations · 1994
Suppose the quasimonotone elliptic system has a supersolution above a subsolution.Then it is shown that there exists a maximal solution in between.Solutions and sub/supersolutions are defined in the spaces C(Q)n and W[(Q)n.The regularity assumptions for the equations are optimal: for fixed off diagonal terms the coupling functions are Caratheodory; for fixed diagonal and space variable these functions are increasing and not necessarily continuous.The basic ingredients are a version of the maximum principle, the Schauder fixed point theorem for the C-ease and an existence theorem of J.L. Lions for the W -case.