Geodesic
On the solution of the Monge–Ampere equation $Z_{xx}Z_{yy}-Z_{xy}^{2}=f(x,y)$ with quadratic right side
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 7 (2011) no. 3, pp. 203-211 Cet article a éte moissonné depuis la source Math-Net.Ru

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For the Monge–Ampere equation $Z_{xx}Z_{yy}-Z_{xy}^{2}=b_{20}x^{2}+b_{11}xy+b_{02}y^{2}+b_{00}$ we consider the question on the existence of a solution $Z(x,y)$ in the class of polynomials such that $Z=Z(x,y)$ is a graph of a convex surface. If $Z$ is a polynomial of odd degree, then the solution does not exist. If $Z$ is a polynomial of $4$-th degree and $4b_{20}b_{02}-b_{11}^{2}>0$, then the solution also does not exist. If $4b_{20}b_{02}-b_{11}^{2}=0$, then we have solutions. 
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     title = {On the solution of the {Monge{\textendash}Ampere} equation $Z_{xx}Z_{yy}-Z_{xy}^{2}=f(x,y)$ with quadratic right side},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
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Yu. Aminov; K. Arslan; B. (Kiliç) Bayram; B. Bulca; C. Murathan; G. Öztürk. On the solution of the Monge–Ampere equation $Z_{xx}Z_{yy}-Z_{xy}^{2}=f(x,y)$ with quadratic right side. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 7 (2011) no. 3, pp. 203-211. http://geodesic.mathdoc.fr/item/JMAG_2011_7_3_a0/

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