We consider the problem −Δu = c0K(x)upε, u > 0 in Ω, u = 0 on δΩ, where Ω is a smooth, bounded domain in ℝN, N ≥ 3, c0 = N(N − 2), pε = (N + 2)/(N − 2) − ε and K is a smooth, positive function on . We prove that least-energy solutions of the above problem are non-degenerate for small ε > 0 under some assumptions on the coefficient function K. This is a generalization of the recent result by Grossi for K ≡ 1, and needs precise estimates and a new argument.

We show the existence and non-existence of positive solutions to a system of singular elliptic equations with the Dirichlet boundary condition.

Some of the proofs in the above paper are incomplete.

The pressure term in the incompressible elasticity equation needs to be considered and estimated in order to pass to the limit in the homogenization process. This will require Sections 2.2 and 3.2 to be rewritten.

A corrected version will be submitted in due course.