Aminov, Yu A.Bayram, Bengü KılıçÖztürk, Günay2022-02-182022-02-182011Aminov, Y. vd. (2011). "On the solution of the monge-ampere equation ZxxZyy-Z2xy = f(x,y) with quadratic right side". Journal of Mathematical Physics, Analysis, Geometry, 7(3), 203-211.1812-94711817-5805http://hdl.handle.net/11452/24534For the Monge-Ampere equation Z(xx)Z(yy) - Z(xy)(2) = b(20)(x2)+b(11).xy+b(02y)(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.eninfo:eu-repo/semantics/closedAccessMathematicsPhysicsMonge-Ampere equationPolynomialConvex surfaceArticle0003011732000012-s2.0-8488343547420321173Mathematics, appliedMathematicsPhysics, mathematicalHessian; Entire Solution; Monge-Ampère Equation