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Volume 32, Issue 3
The Liouville Type Theorem for a System of Nonlinear Integral Equations on Exterior Domain

Rong Yin, Jihui Zhang & Xudong Shang

DOI: 10.4208/jpde.v32.n3.1

J. Part. Diff. Eq., 32 (2019), pp. 191-206.

Published online: 2019-10

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  • Abstract

In this paper we are concerned with a system of nonlinear integral equations on the exterior domain under the suitable boundary conditions. Through the method of moving planes in integral forms which has some innovative ideas we obtain that the exterior domain is radial symmetry and a pair of positive solutions of the system is radial symmetry and monotone non-decreasing. Consequently, we can obtain the corresponding Liouville type theorem about the solutions.

  • Keywords

System of integral equations exterior domain symmetry monotonicity Liouville type theorem.

  • AMS Subject Headings

35A15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yinrong1997@hotmail.com (Rong Yin)

zhangjihui@njnu.edu.cn (Jihui Zhang)

xudong-shang@163.com (Xudong Shang)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-32-191, author = {Yin , RongZhang , Jihui and Shang , Xudong}, title = {The Liouville Type Theorem for a System of Nonlinear Integral Equations on Exterior Domain}, journal = {Journal of Partial Differential Equations}, year = {2019}, volume = {32}, number = {3}, pages = {191--206}, abstract = {

In this paper we are concerned with a system of nonlinear integral equations on the exterior domain under the suitable boundary conditions. Through the method of moving planes in integral forms which has some innovative ideas we obtain that the exterior domain is radial symmetry and a pair of positive solutions of the system is radial symmetry and monotone non-decreasing. Consequently, we can obtain the corresponding Liouville type theorem about the solutions.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v32.n3.1}, url = {http://global-sci.org/intro/article_detail/jpde/13339.html} }
TY - JOUR T1 - The Liouville Type Theorem for a System of Nonlinear Integral Equations on Exterior Domain AU - Yin , Rong AU - Zhang , Jihui AU - Shang , Xudong JO - Journal of Partial Differential Equations VL - 3 SP - 191 EP - 206 PY - 2019 DA - 2019/10 SN - 32 DO - http://doi.org/10.4208/jpde.v32.n3.1 UR - https://global-sci.org/intro/article_detail/jpde/13339.html KW - System of integral equations KW - exterior domain KW - symmetry KW - monotonicity KW - Liouville type theorem. AB -

In this paper we are concerned with a system of nonlinear integral equations on the exterior domain under the suitable boundary conditions. Through the method of moving planes in integral forms which has some innovative ideas we obtain that the exterior domain is radial symmetry and a pair of positive solutions of the system is radial symmetry and monotone non-decreasing. Consequently, we can obtain the corresponding Liouville type theorem about the solutions.

Rong Yin , Jihui Zhang & Xudong Shang . (2019). The Liouville Type Theorem for a System of Nonlinear Integral Equations on Exterior Domain. Journal of Partial Differential Equations. 32 (3). 191-206. doi:10.4208/jpde.v32.n3.1
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