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- Title
Monotonicity for fractional Laplacian systems in unbounded Lipschitz domains.
- Authors
Ma, Lingwei; Zhang, Zhenqiu
- Abstract
In this paper, we first establish a narrow region principle for systems involving the fractional Laplacian in unbounded domains, which plays an important role in carrying on the direct method of moving planes. Then combining this direct method with the sliding method, we derive the monotonicity of bounded positive solutions to the following fractional Laplacian systems in unbounded Lipschitz domains Ω { (−Δ)su = ƒ(u,v), in Ω, (−Δ)tv = g(u,v), in Ω, u,v ≡ 0, on Rn \ Ω without any decay assumptions on the solution pair (u,v) at infinity.
- Subjects
INFINITY (Mathematics)
- Publication
Discrete & Continuous Dynamical Systems: Series A, 2021, Vol 41, Issue 2, p537
- ISSN
1078-0947
- Publication type
Article
- DOI
10.3934/dcds.2020268