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The aim of this paper is to show that Liouville type property is a sufficient and necessary condition for the regularity of weak solutions of nonlinear elliptic systems of the higher order.

Abstract. The aim of this paper is to show that Liouville type property is a sufficient and necessary condition for the regularity of weak solutions of nonlinear elliptic systems of the higher order.

In this paper we study of the existence of solutions for a class of elliptic system with nonlocal term in R N . The main tool used is the variational method, more precisely, the Mountain Pass Theorem.