Volume 29, Issue 3
The Method of Moving Planes for Integral Equation in an Extremal Case

J. Part. Diff. Eq., 29 (2016), pp. 246-254.

Published online: 2016-09

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• Abstract
In this paper, we study the symmetry results and monotonicity of solutions for an integral equation $$u(x)=-c_N∫_{\mathbb{R}^N}e^{u(y)}log|x-y|dy$$ in an external case.
• Keywords

Integral equation radial symmetry the method of moving planes

35R09, 35B06

@Article{JPDE-29-246, author = {Ying and Wang and yingwang00@126.com and 4374 and Department of Mathematics, Jiangxi Normal University, Nanchang, Jiangxi 330022, China and Ying Wang and Jian and Wang and jianwang2007@126.com and 4375 and Institute of Technology, East China Jiaotong University, Nanchang, Jiangxi 330022, China and Jian Wang}, title = {The Method of Moving Planes for Integral Equation in an Extremal Case}, journal = {Journal of Partial Differential Equations}, year = {2016}, volume = {29}, number = {3}, pages = {246--254}, abstract = { In this paper, we study the symmetry results and monotonicity of solutions for an integral equation $$u(x)=-c_N∫_{\mathbb{R}^N}e^{u(y)}log|x-y|dy$$ in an external case.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v29.n3.6}, url = {http://global-sci.org/intro/article_detail/jpde/5091.html} }
TY - JOUR T1 - The Method of Moving Planes for Integral Equation in an Extremal Case AU - Wang , Ying AU - Wang , Jian JO - Journal of Partial Differential Equations VL - 3 SP - 246 EP - 254 PY - 2016 DA - 2016/09 SN - 29 DO - http://doi.org/10.4208/jpde.v29.n3.6 UR - https://global-sci.org/intro/article_detail/jpde/5091.html KW - Integral equation KW - radial symmetry KW - the method of moving planes AB - In this paper, we study the symmetry results and monotonicity of solutions for an integral equation $$u(x)=-c_N∫_{\mathbb{R}^N}e^{u(y)}log|x-y|dy$$ in an external case.