Solutions of Elliptic Equations ΔU+K(x)e<sup>2u</sup>=f(x)

Solutions of Elliptic Equations ΔU+K(x)e<sup>2u</sup>=f(x)

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