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

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We study the problem of the existence and nonexistence of positive solutions to the superlinear second-order divergence type elliptic equation with measurable coefficients −∇⋅a⋅∇u=up(*), p>1, in an unbounded cone-like domain G⊂RN(N⩾3). We prove that the critical exponent p*(a,G)=inf{p>1:(*)has a positive supersolution at infinity inG} for a nontrivial cone-like domain is always in (1,NN−2) and depends both on the geometry of the domain G and the coefficients a of the equation.