Fast decay estimates for integrable solutions of the Lane–Emden type integral systems involving the Wolff potentials
Fast decay estimates for integrable solutions of the Lane–Emden type integral systems involving the Wolff potentials
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DOI：
10.1016/j.jfa.2012.09.012
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发表时间：
2012-12
影响因子：
1.7
通讯作者：
Shan Sun;Y. Lei
中科院分区：
文献类型：
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作者：
Shan Sun;Y. Lei
本文研究了Rn中包含Wolff势的积分系统正可积解的渐近估计，其中1<γ <$2，β>0，βγ<n.另外，p，q>1满足临界条件γ− 1 p +γ−1+γ− 1 q +γ−1=n−βγn，且R1（x），R2（x）在Rn中是有界的.对于径向解，最近建立了衰变率，|X| →∞。当解没有径向结构时，渐近性态更为复杂。我们使用迭代技术来估计可积解u和v的衰减率，|X| →∞。此外，作为该结果的推论，我们还得到了其他Lane-Emden型偏微分方程组和积分系统的渐近估计，包括γ-拉普拉斯系统、高阶偏微分方程组和涉及Riesz势的积分系统。
In this paper, we study the asymptotic estimates of the positive integrable solutions of an integral system involving the Wolff potentials in RnHere 1<γ⩽2, β>0 and βγ<n. In addition, p,q>1 satisfy the critical condition γ−1p+γ−1+γ−1q+γ−1=n−βγn, and R1(x), R2(x) are double bounded in Rn. For the radial solutions, the decay rates were established recently when |x|→∞. When the solutions have no radial structure, the asymptotic behavior is more complicated. We use an iteration technique to estimate the decay rates of the integrable solutions u and v as |x|→∞. Furthermore, as the corollaries of this result, we also obtain the asymptotic estimates of other Lane–Emden type PDE systems and integral systems, including the γ-Laplace system, the higher-order PDE system, and the integral system involving the Riesz potentials.