一类m-Laplacian方程爆破整体解的存在性和不存在性

摘要

本文研究了RN中的m-Laplacian方程△mu=ρ(x)f(u),x∈RN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 = p(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.