Nonexistence of anti-symmetric solutions for fractional Hardy–Hénon system
Nonexistence of anti-symmetric solutions for fractional Hardy–Hénon system
We study anti-symmetric solutions about the hyperplane $\{x_n=0\}$ for the following fractional Hardy–Hénon system: \[ \left\{\begin{array}{@{}ll} (-\Delta)^{s_1}u(x)=|x|^\alpha v^p(x), & x\in\mathbb{R}_+^n, \\ (-\Delta)^{s_2}v(x)=|x|^\beta u^q(x), & x\in\mathbb{R}_+^n, \\ u(x)\geq 0, & v(x)\geq 0,\ x\in\mathbb{R}_+^n, \end{array}\right. \] where $0< s_1,s_2<1$ , $n>2\max \{s_1,s_2\}$ . Nonexistence of anti-symmetric solutions are obtained in some appropriate …