On a problem for Wardʼs equation with a Mittag–Leffler potential

We solve a problem for a type of non-linear partial differential equation (“Wardʼs equation”). This is an equation arising naturally in the study of Coulomb gases and random normal matrix ensembles [4]. In this paper, we consider a problem for Wardʼs equation whose solutions are precisely the well-known Mittag–Leffler functions. Our solution to this problem generalizes certain results obtained in [4].