Journal article
Radial symmetry results for systems of integral equations on $${\Omega\subset {\mathbb{R}}^n}
Manuscripta mathematica, Vol.137(3), pp.317-330
03/2012
DOI: 10.1007/s00229-011-0465-6
Abstract
The main purpose of this paper is to investigate positive solutions of the following system of integral equations with weight Riesz potential on Ω:
$$\left\{\begin{array}{ll} u(x)=\int\limits_{\Omega}{|x|^{-\alpha}|x-y|^{-\mu}|y|^{-\beta}}{u^a(y)v^b(y)}dy,\\ v(x)=\int\limits_{\Omega}{|x|^{-\gamma}|x-y|^{-\nu}|y|^{-\kappa}}{u^c(y)v^d(y)}dy,\\ \end{array} \right.$$
where a, b, c, d, α, β, γ, κ, μ, ν are constants. With the method of moving planes, we establish the symmetry of both the solution and the bounded C
1 domain Ω if u and v are constants on ∂Ω. Moreover, we also give a symmetry result for systems of integral equations with weight Riesz potential on exterior domains.
Details
- Title: Subtitle
- Radial symmetry results for systems of integral equations on $${\Omega\subset {\mathbb{R}}^n}
- Creators
- Xiaotao Huang - Department of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing 210016 People’s Republic of ChinaDongsheng Li - College of Science Xi’an Jiaotong University Xi’an 710049 ChinaLihe Wang - Department of Mathematics University of Iowa Iowa City IA 52242-1419 USA
- Resource Type
- Journal article
- Publication Details
- Manuscripta mathematica, Vol.137(3), pp.317-330
- Publisher
- Springer-Verlag
- DOI
- 10.1007/s00229-011-0465-6
- ISSN
- 0025-2611
- eISSN
- 1432-1785
- Language
- English
- Date published
- 03/2012
- Academic Unit
- Mathematics
- Record Identifier
- 9984083895602771
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