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The non-local Gel’fand problem, $\Delta v+\lambda e^v/{\int }_{\Omega }{e}^{v}dx=0$ with Dirichlet boundary condition, is studied on an n-dimensional bounded domain Ω. If it is star-shaped, then we have an upper bound of λ for the existence of the solution. We also have infinitely many bendings in λ of the connected component of the solution set in λ,v if Ω is a ball and 3 ≤ n ≤ 9.