  We establish the existence of at least two solutions of the {\it
Prandtl-Batchelor} like elliptic problem driven by a power nonlinearity and a
singular term. The associated energy functional is nondifferentiable and hence
the usual variational techniques do not work. We shall use a novel approach in
tackling the associated energy functional by a sequence of $C^1$ functionals
and a {\it cutoff function}. Our main tools are fundamental elliptic regularity
theory and the mountain pass theorem.
