A priori estimates of stable solutions of the general Hardy-Henon equation in the ball

This paper is devoted to the study of semi-stable radial solutions u∈ H¹(B₁) of -Δu= x^αf(u) in B₁0, where f∈ C¹(R) is a general nonlinearity, $α>-2$ and B₁ is the unit ball of RN, $N>1$. We establish the boudness of such solutions for dimensions 2≤ N<10+4α and sharp pointwise estimates in the case N≥10+4α. In addition, we provide, for this range of dimensions, a large family of semi-stable radially decreasing unbounded H¹(B₁) solutions.