一类半线性分数Laplacian方程多解的存在性问题
THE EXSITENCE OF MULTIPLE SOLUTIONS FOR A CLASS OF SEMILINEAR FRACTIONAL LAPLACIAN EQUATIONS

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.
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