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In this article, we study the existence of the weak solution for superlinear elliptic equations and systems without the Ambrosetti-Rabinowitz condition. The Ambrosetti-Rabinowitz condition guarantees the boundedness of the PS sequence of the functional I for the corresponding problem. We establish the existence of the weak solution for the superlinear elliptic equation by using $(PS)_c$ form of the Mountain pass lemma, and the existence of the weak solution for the superlinear elliptic system by using $(PS)_c^{*}$ form of the Linking theorem.