A Liouville-Type Theorem for Fractional Elliptic Equation with Exponential Nonlinearity

In this paper, we are concerned with stable solutions to the fractional elliptic equation $$\begin{aligned} (-\Delta )^s u=e^u \text{ in } {\mathbb {R}}^{N}, \end{aligned}$$ where $$(-\Delta )^s$$ is Laplacian $$0<s<1$$ . By developing a new technique non-compactly supported test functions, establish nonexistence of provided that $$N<10s$$ This result optimal when $$s\uparrow 1$$ On other hand, believe our can be used study equations/systems involving Laplacian.