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Volume 24, Issue 4
Symmetry and Uniqueness of Solutions of an Integral System

Zhengce Zhang & Minji Jiang

DOI: 10.4208/jpde.v24.n4.6

J. Part. Diff. Eq., 24 (2011), pp. 351-360.

Published online: 2011-11

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  • Abstract

In this paper, we study the positive solutions for a class of integral systems and prove that all the solutions are radially symmetric and monotonically decreasing about some point. Moreover, we also obtain the uniqueness result for a special case. We use a new type of moving plane method introduced by Chen-Li-Ou [1]. Our new ingredient is the use of Hardy-Littlewood-Sobolev inequality instead of Maximum Principle.

  • Keywords

Radial symmetry uniqueness integral system moving plane method

  • AMS Subject Headings

35J65 35J25 35B50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-24-351, author = {Zhengce Zhang and Minji Jiang }, title = {Symmetry and Uniqueness of Solutions of an Integral System}, journal = {Journal of Partial Differential Equations}, year = {2011}, volume = {24}, number = {4}, pages = {351--360}, abstract = {

In this paper, we study the positive solutions for a class of integral systems and prove that all the solutions are radially symmetric and monotonically decreasing about some point. Moreover, we also obtain the uniqueness result for a special case. We use a new type of moving plane method introduced by Chen-Li-Ou [1]. Our new ingredient is the use of Hardy-Littlewood-Sobolev inequality instead of Maximum Principle.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v24.n4.6}, url = {http://global-sci.org/intro/article_detail/jpde/5216.html} }
TY - JOUR T1 - Symmetry and Uniqueness of Solutions of an Integral System AU - Zhengce Zhang & Minji Jiang JO - Journal of Partial Differential Equations VL - 4 SP - 351 EP - 360 PY - 2011 DA - 2011/11 SN - 24 DO - http://doi.org/10.4208/jpde.v24.n4.6 UR - https://global-sci.org/intro/article_detail/jpde/5216.html KW - Radial symmetry KW - uniqueness KW - integral system KW - moving plane method AB -

In this paper, we study the positive solutions for a class of integral systems and prove that all the solutions are radially symmetric and monotonically decreasing about some point. Moreover, we also obtain the uniqueness result for a special case. We use a new type of moving plane method introduced by Chen-Li-Ou [1]. Our new ingredient is the use of Hardy-Littlewood-Sobolev inequality instead of Maximum Principle.

Zhengce Zhang and Minji Jiang . (2011). Symmetry and Uniqueness of Solutions of an Integral System. Journal of Partial Differential Equations. 24 (4). 351-360. doi:10.4208/jpde.v24.n4.6
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