Nonlinear nonhomogeneous singular problems

We consider a nonlinear Dirichlet problem driven by a nonhomogeneous differential operator with a growth of order ( p- 1) near+8 and with a reaction which has the competing effects of a parametric singular term and a ( p - 1)-superlinear perturbation which does not satisfy the usual Ambrosetti-Rabinowitz condition. Using variational tools, together with suitable truncation and strong comparison techniques, we prove a bifurcation-type theorem that describes the set of positive solutions as the parameter. moves on the positive semiaxis. We also show that for every. > 0, the problem has a smallest positive solution u *. and we demonstrate the monotonicity and continuity properties of the map lambda -> u(lambda)*.