Geodesic
Solutions of the equation $\Delta u=f(x,y)e^{cu}$ in some special cases
Sbornik. Mathematics, Tome 192 (2001) no. 6, pp. 879-894

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The equation $\Delta u=f(x,y)e^{cu}$ is considered in the case when the coefficient $f(x,y)$ is the absolute value or the square of the absolute value of some holomorphic function. In this case a full description of the general solution of the equation is presented. Several problems usually posed for elliptic equations are also discussed. 
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     author = {I. Kh. Sabitov},
     title = {Solutions of the equation $\Delta u=f(x,y)e^{cu}$ in some special cases},
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     url = {http://geodesic.mathdoc.fr/item/SM_2001_192_6_a5/}
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I. Kh. Sabitov. Solutions of the equation $\Delta u=f(x,y)e^{cu}$ in some special cases. Sbornik. Mathematics, Tome 192 (2001) no. 6, pp. 879-894. http://geodesic.mathdoc.fr/item/SM_2001_192_6_a5/