On the positive radial solutions of a class of singular semilinear elliptic equations
On the positive radial solutions of a class of singular semilinear elliptic equations
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DOI：
10.1016/j.jde.2012.02.017
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发表时间：
2012-07
影响因子：
2.4
通讯作者：
Yinbin Deng;Yi A. Li;Fen Yang
中科院分区：
文献类型：
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作者：
Yinbin Deng;Yi A. Li;Fen Yang
本文考虑如下椭圆型方程其中p>1，n ≠ 3，A（|X|）>0在Rn {0}和B中是可微的（|X|）是Rn <${0}中给定的非负Hölder连续函数。讨论了方程（0.1）在不同初值下正径向解在无穷远点的渐近性态和分离性结构。作为特例，分别得到了哈代方程和一个与Caffarelli-Kohn-Nirenberg不等式有关的方程无穷多个正解的存在性和分离性.
In this paper, we consider the following elliptic equation where p>1, n⩾3, A(|x|)>0 is differentiable in Rn∖{0} and B(|x|) is a given nonnegative Hölder continuous function in Rn∖{0}. The asymptotic behavior at infinity and structure of separation property of positive radial solutions with different initial data for (0.1) are discussed. Moreover, the existence and separation property of infinitely many positive solutions for Hardy equation and an equation related to Caffarelli–Kohn–Nirenberg inequality are obtained respectively, as special cases.