A stability result for elliptic equations with singular nonlinearity and its applications to homogenization problems

We consider model semilinear elliptic equations of the type{−div(A(x)∇u)=σu−λ,u>0inΩ,u∈H01(Ω), where Ω is a bounded domain in RN, N≥1, A∈L∞(Ω)N×N coercive matrix, 0<λ≤1 and σ nonnegative function Lloc1(Ω), or more generally, Radon measure on Ω. discuss H01(Ω)-stability u under minimal assumption apply result to homogenization problems.