On a class of nonlocal elliptic problems via Galerkin method

In this paper we study existence and uniqueness of solutions to some cases of the following nonlocal elliptic problem: −Δu=(g(x,u))α(∫Ωf(x,u))β with zero Dirichlet boundary conditions on a bounded and smooth domain of RN and also when Ω=RN, where α and β are real constants.