一类m-Laplacian方程爆破整体解的存在性和不存在性  

EXISTENCE AND NON-EXISTENCE OF BLOW-UP ENTIRE SOLUTIONS OF A CLASS OF M-LAPLACIAN EQUATIONS

作　　者：辛奎东[1] 陈才生[2] 

机构地区：[1]广东轻工职业技术学院经济系,广州510300 [2]河海大学理学院,南京210098

出　　处：《南京大学学报（数学半年刊）》2012年第1期75-83,共9页Journal of Nanjing University(Mathematical Biquarterly)

摘　　要：本文研究了R^N中的m-Laplacian方程△_mu=ρ(x)f(u),x∈R^N的非负爆破整体解的存在性和不存在性.利用上下解方法得到了解的存在性,在这里并没有对函数f附加单调性的假设;利用积分方程和一个积分条件得到了径向对称解的不存在性.In this paper, we study existence and non-existence of nonnegative blow-up entire solutions of a class of m-laplacian equations △mu=ρ（x）f（u）,x∈RN.The method of getting existence is based on lower and upper solutions techniques without assuming that f is monotonic and by estimates on an associated integral equation and integral condition,we get nonexistence of radial symmetry solutions.

关 键 词：非爆破整体解 上下解方法 

分 类 号：O241.82[理学—计算数学]