Continuity results for parametric nonlinear singular Dirichlet problems

In this paper we study from a qualitative point of view the nonlinear singular Dirichlet problem depending on a parameter λ > 0 that was considered in [32]. Denoting by S λ the set of positive solutions of the problem corresponding to the parameter λ , we establish the following essential properties of S λ : there exists a smallest element array u_λ^* array in S λ , and the mapping λ ↦ array u_λ^* array is (strictly) increasing and left continuous; the set-valued mapping λ ↦ S λ is sequentially continuous.