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

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