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

The Dirichlet problem for $-\Delta \varphi= \mathrm{e}^{-\varphi}$ in an infinite sector. Application to plasma equilibria