An elliptic problem of the Prandtl–Batchelor type with a singularityChoudhuri, Debajyoti (Avtor) Repovš, Dušan (Avtor) elliptic free boundary problemsmountain pass theoremsingularityWe 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.20232023-06-22 13:24:21Članek v reviji147075UDK: 517.9ISSN pri članku: 1687-2770DOI: 10.1186/s13661-023-01747-wCOBISS_ID: 156397059sl