ON THE ELLIPTIC EQUATION <TEX>${\Delta}u+H({\chi})e^{u}$</TEX> = 0 ON COMPACT MANIFOLDS
한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
1996, v.3 no.1, pp.9-18
Jung, Yoon-Tae
(Department of Mathematics, Chosun University)
Kim, Seon-Bu
(Department of Mathematics, Chonam National University)
Shin, Cheol-Guen
(Department of Mathematics, Chosun University)
Jung, Yoon-Tae,
Kim, Seon-Bu,
&
Shin, Cheol-Guen.
(1996). ON THE ELLIPTIC EQUATION <TEX>${\Delta}u+H({\chi})e^{u}$</TEX> = 0 ON COMPACT MANIFOLDS. 한국수학교육학회지시리즈B:순수및응용수학, 3(1), 9-18.
Abstract
In this paper, we consider the existence of a solution to the elliptic nonlinear partial differential equation <TEX>${\Delta}u+H({\chi})e^{u}$</TEX> = 0 (H <TEX>$\neq$</TEX> 0) (1) on a compact manifold without boundary. This equation is related to the problem of a pointwise conformal deformation of metrics on two dimensional compact connected manifolds.(omitted)