Monotonicity for the fractional semi-linear problem in a half space

Wenxiong Chen, Yahong Guo, Leyun Wu

In this paper, we study semilinear fractional equations $$(-\Delta {)}^{s}u(x)=f(u(x))$$ in a half-space and prove that all positive solutions are strictly increasing in the $x_n$-directi…