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）+α△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,α，βare 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+α(△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.