Continuity results for parametric nonlinear singular Dirichlet problems

Abstract

Abstract 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 Sλ the set of positive solutions of the problem corresponding to the parameter λ, we establish the following essential properties of Sλ: there exists a smallest element $\begin{array}{} u_\lambda^* \end{array}$ in Sλ, and the mapping λ ↦ $\begin{array}{} u_\lambda^* \end{array}$ is (strictly) increasing and left continuous; the set-valued mapping λ ↦ Sλ is sequentially continuous.