Year: 1991
Journal of Partial Differential Equations, Vol. 4 (1991), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1991-JPDE-5766
Journal of Partial Differential Equations, Vol. 4 (1991), Iss. 2 : pp. 36–44
Published online: 1991-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: elliptic equations