@Article{JPDE-4-36, author = {}, title = {Solutions of Elliptic Equations ΔU+K(x)e2u=f(x)}, journal = {Journal of Partial Differential Equations}, year = {1991}, volume = {4}, number = {2}, pages = {36--44}, abstract = { In this paper we consider the elliptic equation Δu + K(x)e^{2u} = f(x), which arises from prescribed curvature problem in Riemannian geometry. It is proved that if K(x) is negative and continuous in R², then for any f ∈ L²_{loc} (R²) such that f(x) ≤ K(x), the equation possesses a positive solution. A uniqueness theorem is also given.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5766.html} }