On a Positive Solution for a Class Cooperative Elliptic Systems
Chun‐Lei Tang · Journal of Southwest University · 2008
With the sub-supersolution method and the maximum principle,the existence of a minimal positive solution is proved for the following system-Δu=F/u(x,u,v)+eg(x),-Δv=F/v(x,u,v)+eh(x) in Ω;u,v0 in Ω;and u=v=0 on Ω,with e sufficiently small,where Ω is a bounded smooth domain in RN;F∈C1(Ω×(R+)2, R+);g,h∈C1(Ω);and e is a positive parameter. In addition,it is proved that the problem has no solution for e large enough.