| 摘要: |
| 本文研究了一类半线性分数Laplacian方程{（-△）su=f（x，u），x∈Ωu=0，x∈Rn\Ω在原点附近无穷多解的存在性问题.利用改进的Clark's定理，获得了方程对应的泛函有收敛于零的临界点序列的结果，推广了关于整数阶半线性方程多解的存在性结果. |
| 关键词: 分数Laplacian算子 临界点 无穷多解 Clark's定理 |
| DOI： |
| 分类号:O175.29 |
| 基金项目:国家自然科学基金面上项目（11571268）；陕西省自然科学基础研究计划项目（2017JQ1022）. |
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| THE EXSITENCE OF MULTIPLE SOLUTIONS FOR A CLASS OF SEMILINEAR FRACTIONAL LAPLACIAN EQUATIONS |
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QIAO Hua-ling, WU Yu-mei
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School of Statistics, Xi'an University of Finance and Economics, Xi'an 710061, China
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| Abstract: |
| In this paper,we study the existence of infinitely many solutions near the origin for a class semilinear fractional Laplacian equtions {（-△）su=f（x，u），x∈Ω,u=0，x∈Rn\Ω By improved Clark's theorem, we obtain the result that the corresponding functional of the equation has a critical sequence that converges to zero. The results of the existence of multiple solutions for integral order semilinear equations are generalized. |
| Key words: fractional Laplacian critical infinitely many solutions Clark's theorem |
