Super Polyharmonic Property of Solutions for PDE Systems and Its Applications
Super Polyharmonic Property of Solutions for PDE Systems and Its Applications
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DOI：
10.3934/cpaa.2013.12.2497
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发表时间：
2011-10
期刊：
影响因子：
--
通讯作者：
Wenxiong Chen;Congming Li
中科院分区：
文献类型：
--
作者：
Wenxiong Chen;Congming Li
In this paper, we prove that all the positive solutions for the PDE system (-\Delta)^{k}u_{i} = f_{i}(u_{1},..., u_{m}), x \in R^{n}, i = 1, 2,..., m are super polyharmonic, i.e. (-\Delta)^{j}u_{i} > 0, j = 1, 2,..., k - 1; i = 1, 2,...,m. To prove this important super polyharmonic property, we introduced a few new ideas and derived some new estimates. As an interesting application, we establish the equivalence between the integral system u_{i}(x) = \int_{R^{n}} \frac{1}{|x - y|^{n-\alpha}}f_{i}(u_{1}(y),..., u_{m}(y))dy, x \in R^{n} and PDE system when \alpha? = 2k < n
