Positive solutions for a class of nonlocal problems with possibly singular nonlinearity

We study a class of elliptic problems with homogeneous Dirichlet boundary condition and a nonlinear reaction term f which is nonlocal depending on the Lp-norm of the unknown function. The nonlinearity f can make the problem degenerate since it may even have multiple singularities in the nonlocal variable. We use fixed point arguments for an appropriately defined solution map, to produce multiplicity of classical positive solutions with ordered norms.