On singular elliptic equations involving critical Sobolev exponent

Given a n–dimensional compact Riemannian manifold (M, g) with n ≥ 5, we consider the following semi-linear elliptic equation, where the functions a, b and h are in suitable Lebesgue spaces, 2 < q < N and λ > 0 a real parameter, f is a smooth positive function and the operator P_g is coercive. Under some additional conditions, we obtain results concering the existence of strong solutions of the above equation in H²₂ (M).