Boundary Behavior of Positive Solutions of Semilinear Elliptic Equations with Negative Exponent

We estimate the Hausdorff dimension of a subset of the unit sphere where a positive solution of a semilinear elliptic equation with source term of negative exponent in the unit ball grows faster than a prescribed order. Also, the sharpness of our estimate is shown by proving the existence of a positive solution growing faster than a prescribed order on a given subset of the unit sphere.