论文标题
对于关键的哈特里方程的解决方案的非修饰性
Nondegeneracy of solutions for a critical Hartree equation
论文作者
论文摘要
本文的目的是证明当$μ> 0 $接近$ 0 $，$$-ΔU= \ left时（I_μ\ ast） u^{2^{\ ast}_μ} \ right） i_μ（x）= \ frac {γ（\fracμ{2}）}} {γ（\ frac {n-μ} {2} {2} {2}）π^{\ frac {n} {2} {2} {2}}}}} 2^{n-μ} $ 2^{\ ast}_μ= \ frac {2 {n-μ}} {n-2} $是由于强壮的littlewood-sobolev不等式而导致的临界指数。
The aim of this paper is to prove the nondegeneracy of the unique positive solutions for the following critical Hartree type equations when $μ>0$ is close to $0$, $$ -Δu=\left(I_μ\ast u^{2^{\ast}_μ}\right)u^{{2}^{\ast}_μ-1},~~x\in\mathbb{R}^{N}, $$ where $ I_μ(x)=\frac{Γ(\fracμ{2})}{Γ(\frac{N-μ}{2})π^{\frac{N}{2}}2^{N-μ}|x|^μ} $ is the Riesz potential and $2^{\ast}_μ=\frac{2{N-μ}}{N-2}$ is the upper critical exponent due to the Hardy-Littlewood-Sobolev inequality.
