In this talk we review some results about the nonlinear elliptic pdes originating from field theories. First we recall some elliptic pdes with related results arising from the classical Abelian Higgs model. Then we review the pdes appear in the Abelian and non-Abelian Chern—Simons—Higgs models and present some existence results. In particular, we report some recent results concerning the existence of doubly periodic solutions. At last, we mention some related open questions.

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