TY - JOUR
T1 - Solutions of Elliptic Equations ΔU+K(x)e<sup>2u</sup>=f(x)
JO - Journal of Partial Differential Equations
VL - 2
SP - 36
EP - 44
PY - 1991
DA - 1991/04
SN - 4
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5766.html
KW - elliptic equations
KW - prescribed curvature problem
KW - monotone operators
KW - Kato's inequality
AB -  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.