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∈Ω, u=0,x∈R^n\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∈R^n\Ωimproved 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.