Positive solutions to sublinear second-order divergence type elliptic equations in cone-like domains

We study the existence and nonexistence of positive solutions to a sublinear (p<1)(p<1) second-order divergence type elliptic equation (*):−∇⋅a⋅∇u=up in unbounded cone-like domains CΩCΩ. We prove the existence of the critical exponentp*(a,CΩ)=sup{p<1:(*)has a positive supersolution at infinity inCΩ}, which depends on the geometry of the cone CΩCΩ and the coefficients a of the equation.