奇异p-Laplace方程的正整体解的存在性  

The existence of positive entire solutions of a class of singular, p-Laplace equations

作　　者：吴炯圻[1] 

机构地区：[1]漳州师范学院数学系,漳州363000

出　　处：《纯粹数学与应用数学》2005年第2期103-110,共8页Pure and Applied Mathematics

基　　金：国家自然科学基金资助课题(10271056);福建省自然科学基金资助课题(F00018).

摘　　要：研究如下散度型奇异非线性p-Laplace方程Δpu:=∑Ni=1Di(|Du|)p-2Diu)=f(|x|,u,|du|)u-β在RN(N≥3)上的正整体解,此处p>1,β>0是实数,f:[0,∞)×(0,∞)×[0,∞)→(-∞,+∞)是连续函数,给出了该方程具有多个有界的径向对称的正整体解u(x)满足lim|x|→∞u(x)=常数的条件.In this paper N -dimensional singular, p -Laplace equations of the form Δpu：=N∑i=1 Di（｜Du｜）p-2Diu）=f（｜x｜,u,｜du｜）u-β, x∈ R^N（N≥3） are considered, where p〉1,β〉0, x = （x1,…,XN）, ｜x｜ = （x2^2 ＋ ... ＋ x^2N）^1/2 , and ,f：[0,∞）×（0,∞）×[0,∞）→（-∞,＋∞） is a continuous function. Some sufficient conditions are obtained for the existence of infinitely many radical positive entire solutions of the equation each of which approaches to a positive constant as ｜x｜→∞.

关 键 词：奇异的 非线性方程 P-LAPLACE算子 正整体解 不动点定理 

分 类 号：O175.29[理学—数学] O175.14[理学—基础数学]