中文摘要：

本文研究在Dirichlet边界条件下分数阶椭圆型方程（-△）^su=λf（x，u）的解的多重性．利用非线性项，在零点处和无穷远处的渐近性态，在Ambrosetti．Rabinowitz条件不满足的情形，应用山路定理和适当的截断技巧，对于所有的参数A〉O得到一个正解和一个负解．

英文摘要：

This paper deals with the multiplicity of solutions for some fractional elliptic equation （-A）Su = ）,f（x, u） under Dirichlet boundary condition. By using the asymptotic behavior of the nonlinearity f at zero and infinity without Ambrosetti-Rabinowitz growth condition, we apply mountain pass theorem and suitable truncation to obtain the existence of one positive solution and one negative solution for all the parameter A 〉 0.