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 lambda > 0 that was considered in [32]. Denoting by S-lambda the set of positive solutions of the problem corresponding to the parameter lambda, we establish the following essential properties of S lambda: (i) there exists a smallest element u(lambda)* in S-lambda, and the mapping lambda -> u(lambda)* is (strictly) increasing and left continuous; (ii) the set-valued mapping lambda -> S-lambda is sequentially continuous.