Depending on what precisely you are interested in, one place to start may be

H. Berestycki, T. Gallouët, O. Kavian.  Équations de champs scalaires euclidiens non linéaires dans le plan. C. R. Acad. Sci. Paris Sér. I Math. 297 (1983), no. 5, 307–310.

(also depending on the specific questions of interest, you might find it useful to look at, e.g., C. Alves, M. Souto, M. Montenegro. Existence of a ground state solution for a nonlinear scalar field equation with critical growth. Calc. Var. Partial Differential Equations 43 (2012), no. 3-4, 537–554).