Uniqueness and stability in an inverse problem for a Poisson’s equation

Consider the Poisson’s equation Ψ″ (x) = −e ^v−Ψ + e ^Ψ−v − N(x) with the Dirichlet boundary data, and we mainly investigate the inverse problem of determining the unknown function N(x) from a parameter function family. Some uniqueness and stability results in the inverse problem are obtained. This work was partially supported by the National Natural Science Foundation of China (Grant No. 10626017), the Science Foundation of the Education Committee of Heilongjiang Province (Grant No. 11511276) and the Foundation of Heilongjiang Province (Grant No. LBH-Q05114)