A Class of Singular Coupled Systems of Superlinear Monge-Ampère Equations  

作　　者：Mei-qiang FENG 

机构地区：[1]School of Applied Science,Beijing Information Science&Technology University,Beijing 100192,China

出　　处：《Acta Mathematicae Applicatae Sinica》2022年第4期925-942,共18页应用数学学报（英文版）

基　　金：supported by Beijing Natural Science Foundation under Grant No.1212003;the Promoting the Classified Development of Colleges and Universities-application and Cultivation of Scientific Research Awards of BISTU under Grant No.2021JLPY408。

摘　　要：In this paper,we analyze the existence,multiplicity and nonexistence of nontrivial radial convex solutions to the following system coupled by singular Monge-Ampère equations{det D^(2)u_(1)=λh_(1)f_(1)(-u_(2))inΩ,det D^(2)u2=λh_(2)f_(2)(-u_(1)),u_(1)=u_(2)=0,onəΩinΩfor a certain range ofλ>0,hi are weight functions,f_(i)are continuous functions with possible singularity at 0 and satisfy a combined N-superlinear growth at∞,where i∈{1,2},Ωis the unit ball in N.We establish the existence of a nontrivial radial convex solution for smallλ,multiplicity results of nontrivial radial convex solutions for certain ranges ofλ,and nonexistence results of nontrivial radial solutions for the caseλ≥1.The asymptotic behavior of nontrivial radial convex solutions is also considered.

关 键 词：Two coupled Monge-Ampère equations Combined N-superlinear growth at∞ Singular weight functions EXISTENCE multiplicity and nonexistence Asymptotic behavior 

分 类 号：O175[理学—数学]