Browsing by Author "Aminov, Yu A."
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Item On the solution of the monge-ampere equation ZxxZyy-Z2xy = f(x,y) with quadratic right side(B Verkin Inst Low Temperature Physics & Engineering Nas Ukra, 2011) Aminov, Yu A.; Bayram, Bengü Kılıç; Öztürk, Günay; Arslan, Kadri; Bulca, Betül; Murathan, Cengizhan; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0001-5861-0184; 0000-0002-1440-7050; ABH-3658-2020; AAG-7693-2021; AAG-8775-2021; 6603079141; 35226209600; 6506718146For 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.