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A problem of prescribing Gaussian curvature on

Authors:	Sulbha Goyal Vinod Goyal

Institution:	Department of Mathematics, Tuskegee University, Tuskegee, Alabama 36088 Vinod Goyal ; Department of Mathematics, Tuskegee University, Tuskegee, Alabama 36088

Abstract:	A class of functions and the corresponding solutions of $\begin{displaymath}\Delta u + K(x)e^{2u}=1\end{displaymath}$ are obtained as a special case of the solutions of $\begin{displaymath}\Delta^mu+K(x)e^{au}=f(x),\qquad x=(x_1,x_2,\dots,x_n),\end{displaymath}$ where $\Delta^m$ is defined as $\Delta(\Delta^{m-1})$ .

Keywords:	Laplace operator Gaussian curvature conformally equivalent metric

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