一类具临界指数的分数阶拉普拉斯方程对称解的存在性

Existence of symmetry solutions for a fractional Laplacian equation with critical nonlinearity

研究了一类分数阶拉普拉斯方程(-Δ)'u+u=|u|^(2*(s)-2)u+f(x,u),x∈R^N解的存在性问题.其中,2*(s)=2N/(N-2s),N>2s,s∈(0,1),函数f:R^N×R→R对于u次临界增长.运用变分方法建立了方程对称解的存在性定理.

The existence of solutions for the following nonlocal fractional Laplacian equation was studied,(-Δ)'u+u=|u|^(2*(s)-2)u+f(x,u),x∈R^N with critical exponent 2*(s)=2N/(N-2s),N>2s,s∈(0,1). f: R^N× R →R had subcritical growth with respect to u. The existence of symmetry solutions for the equation was obtained by using variational method.