Qualitative properties of solutions for an integral equation
Qualitative properties of solutions for an integral equation
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DOI：
10.3934/dcds.2005.12.347
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发表时间：
2003-07
影响因子：
1.1
通讯作者：
Wenxiong Chen;Congming Li;B. Ou
中科院分区：
文献类型：
--
作者：
Wenxiong Chen;Congming Li;B. Ou
设$n$是一个正整数，且$0 < \alpha < n。$本文研究了更一般的积分方程u（x）= \int_{R^n} \frac{1}{|X-Y| ^{n-\alpha}} K（y）u（y）^p dy.我们建立正则性，径向对称性和单调性的解决方案。我们还考虑亚临界情况下，超临界情况下，在所有情况下的奇异解，并获得这些解决方案的定性性质。
Let $n$ be a positive integer and let $ 0 < \alpha < n.$ In this paper, we study more general integral equation $ u(x) = \int_{R^n} \frac{1}{|x-y|^{n-\alpha}} K(y) u(y)^p dy. We establish regularity, radial symmetry, and monotonicity of the solutions. We also consider subcritical cases, super critical cases, and singular solutions in all cases; and obtain qualitative properties for these solutions.