Abstract :
This paper is devoted to the study of semi-stable radial solutions u ∈ H1(B1) of − u = g(u) in B1 \{0},
where g ∈ C1(R) is a general nonlinearity and B1 is the unit ball of RN. We establish sharp pointwise
estimates for such solutions. As an application of these results, we obtain optimal pointwise estimates for
the extremal solution and its derivatives (up to order three) of the semilinear elliptic equation− u = λf (u),
posed in B1, with Dirichlet data u|∂B1 = 0, where f is a continuous, positive, nondecreasing and convex
function on [0,∞) such that f (s)/s→∞as s→∞. In addition, we provide, for N 10, a large family
of semi-stable radially decreasing unbounded H1(B1) solutions.
© 2012 Elsevier Inc. All rights reserved.
