A class of nonlinear partial elliptic equations is studied in this paper. At first, the functional Φ can be established according to the elliptic equations, and the critical points of the functional Φ are the solutions of the elliptic system. Second, special linking theorem for the equations is constructed under some conditions, and the minimax theorem is used. At last the functional Φ can be proved to have at least three critical points. So we can have a conclusion that there has been at least three nontrivial solutions of a class of elliptic equations.
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