Positivity for a Strongly Coupled Elliptic System by Green Function Estimates

摘要

The authors will consider elliptic systems of the following type: L(1)u = f -(epsilon)g(.,v,(Delta)v) in Omega, L(2)v = f in Omega, u = v = 0 on boundary of Omega, where L(1) and L(2) are two (possibly different) second order elliptic operators. The authors suppose that for some c > 0 g(x,v,p) = or < c(v + (verticle stroke)) for all (x,v,p) a member of Omega(bar) x R(sup +) x R(sup n). The aim of the paper is to show the existence of a positive constant epsilon(0) such that u is positive whenever f is positive and epsilon a member of (bracket)0,epsilon(0)).