R^N上奇异非线性多调和方程的正整体解  

ON POSITIVE ENTIRE SOLUTIONS TO SINGULAR, NONLINEAR POLY-HARMONIC EQUATIONS IN R^N(N ≥ 3)

作　　者：吴炯圻[1] 

机构地区：[1]漳州师范学院数学系,福建漳州363000

出　　处：《系统科学与数学》2004年第3期332-339,共8页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(19871068);福建省自然科学基金(F00018)资助课题.

摘　　要：本文研究形如△((△nu)(p-1)+)=f(|x|,u,|(?)u|)u-β,x∈RN的奇异非线性多调和方程在RN上的正整体解,此处P>1,β≥0是常数,n是自然数,f:R+× R+×R+→R+是一个连续函数, ξδ*:=sign(ξ)·|ξ|δ,,ξ∈R,δ>0,给出了该类方程具有无穷多个其渐进阶刚好为|x|2n的正整体解的充分条件与必要条件.这些结论可以推广到更一般的方程.In this paper N-dimensional singular, nonlinear poly-harmonic equations of the following form △((△nu)(p-1)△)=f(|x|,u,|△u|)u-β, x∈RN are considered, where p > 1, β ≥0, n is an integer (n ≥ 1), ξδ := sign(ξ) · |ξ|δ, ξ ∈ R, δ > 0. and f : R+ × R+ × R+ → R+ is a continuous function. Some sufficient conditions and necessary conditions are obtained for the existence of infinitely many positive symmetric entire solutions which are asymptotic to positive constant multiples of |x|2n as |x| → ∞. The results can be extended to certain equations of more general form.

关 键 词：非线性多调和方程 正整体解 不动点定理 LAPLACE算子 奇异方程 

分 类 号：O241[理学—计算数学]