Combined effects of singular and sublinear nonlinearities in some elliptic problems

We consider a parametric singular Dirichlet equation, with the singular term u−γu−γ appearing in the left-hand side. We establish the existence and nonexistence of positive solutions as the parameter λ>0λ>0 and the exponent γ>0γ>0 of the singularity vary. In particular, we show that for all λ>0λ>0 and all γ⩾1γ⩾1, the problem has no positive solution. Our approach combines truncation arguments with the method of upper and lower solutions.