Nonlinear Elliptic Equations with Singular Terms and Combined Nonlinearities

We consider nonlinear elliptic Dirichlet problems with a singular term, a concave (i.e., (p − 1)-sublinear) term and a Carathéodory perturbation. We study the cases where the Carathéodory perturbation is (p − 1)-linear and (p − 1)-superlinear near +∞. Using variational techniques based on the critical point theory together with truncation arguments and the method of upper and lower solutions, we show that if the L ^∞-coefficient of the concave term is small enough, the problem has at least two nontrivial smooth solutions.