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

Abstract

We establish the existence of at least two solutions of the 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 cutoff function. Our main tools are fundamental elliptic regularity theory and the mountain pass theorem.