Existence Of Entire Positive Convex Radial Large Solutions To The Monge-Ampère Type Equation And Systems

This paper is concerned with existence and estimates of entire positive convex radial large solutions for a class of Monge-Ampere type equations and systems.Our approach is based on nonlinear transformation?a monotone iterative method?Arzela-Ascoli theorem and a truncation technique.At first,we introduce the research background.In the second place,using the above four methods,we prove the existence of entire radial large solutions of the Monge-Ampere type equation det D²u?x?+??u=a??x??f?u??x?R^N,and systems???,Then extend it to the general system equations.where D²u?x?is the Hessian matrix of u?x?,det D²u?x?is the Monge-Ampere operator,? is Laplace operator,???are positive constants,a,b:R^N?[0,?)are continuous?f,g,:[0,?)?[0,?)are continuous and non-decreasing,u,u ? C²?R^N?.The third part is to study the case with gradient terms based on the second part,which are the folloing equation det D²u?x?+p??x????u?^N+?(?u+N?x?^N-1p??X????u?)=a??x??f?u?,x?R^N.and systems???,where the conditions of a,b,f,g are changeless,p,q:R^N?[0,?)are continuous.