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

The purpose of this paper is to investigate the existence of entire positive radial large solutions to Monge-Ampère type equations and systems.The thesis includes three parts.In Section 1,we introduce the significance and status at home and abroad of our researches.In Section 2,by a monotone iterative method and Arzela-Ascoli theorem,we ob-tain the existence and estimates of entire convex radial large solutions to the following nonlinear partial differential equations of the Monge-Ampère type detD2u(x)= α△u + a(|x|)f(u),x∈ RN,and systems Here the so-called big solution is that,when |x| →∞,solution tend to +∞.where u ∈C2(RN))D2u(x)denotes the Hessian of u(x),detD2u is the so-called Monge-Ampère operator,△ is the classical Laplace operator,N ≥ 2,α,β are positive constants and a,b:RN→[0,∞)are continuous,f,g:[0,∞)→[0,∞)are continuous and non-decreasing.In Section 3,We can see that Section 2 can be extended to the following Monge-Ampère type equations detD2u(x)+ p(|x|)|▽u|N=α△u + a(|x|)f(u)+ αN|x|N-1p(|x|)|▽u|,x∈ RN and systems where p,q:RN→[0,∞)are continuous.