Existence and Uniqueness for the Fractional Gelfand Equation in $\mathbb{R}$

Florian P. Lanz, Enno Lenzmann

We prove existence, symmetry and uniqueness of solutions to the fractional Gelfand equation $$ (-Δ)^s u = e^u \quad \mbox{in $\mathbb{R}$} \quad \mbox{with} \quad \int_{\mathbb{R}}…