A study of the Prandtl Batchelor problem using variational method

In this paper, we investigate the existence of nontrivial weak solutions for the Prandtl-Batchelor type free boundary value elliptic problem driven by a power nonlinearity. The algebraic topology approach will be used to establish the existence of solutions of approximate problem, while variational techniques will be used to determine the existence of major problem solutions. In the process several classical results are improved.