An elliptic problem of the Prandtl–Batchelor type with a singularity

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