In this paper we concerned ourselves with non-local fractional elliptic equation based on using Mountain Pass theorem, Ekeland Variation principle and Saddle Point theorem. We gain an existence and multiple solutions for this equation near resonance with principal eigenvalue.%利用山路引理、Ekeland 变分原理及鞍点定理，得到了一类非局部分数阶椭圆型方程在主特征值附近解的多重性。
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