The Dirichlet problem for $-\hat{I}”\ddot{I}†={\mathrm{e}}^{-\ddot{I}†}$ in an infinite sector. Application to plasma equilibria

Abstract

We consider here a nonlinear elliptic equation in an unbounded sectorial domain of the plane. We prove the existence of a minimal solution to this equation and study its properties. We infer from this analysis some asymptotics for the stationary solution of an equation arising in plasma physics.