A Liouville type Theorem for an integral system

By Li Ma, Dezhong Chen. 2006

114 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/c7124bbf58f6681b2b8698a7c97fa47990c6d72d

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In Applied Mathematics

1. Wenxiong CHEN *
2. Congming LI #
3. Li Ma
4. Xiaohui Yu
5. Dezhong Chen
6. Alexander Quaas
7. Guanfeng Li
8. Aliang Xia

In Computational Theory and Mathematics

1. Congming LI #
2. Wenxiong CHEN *
3. Guanfeng Li
4. Aliang Xia
5. Alexander Quaas
6. Xiaohui Yu
7. Li Ma
8. Dezhong Chen

Citations in the corpus

• Symmetry and non-existence of solutions for a nonlinear system involving the fractional Laplacian (2015, background): “For more Liouville type theorems, please see [7, 16, 17, 18, 19, 21, 22, 23, 28] and the references therein.”
• Super Polyharmonic Property of Solutions for PDE Systems and Its Applications (2011, methodology): “There are many more applications of this method to integral systems, and the interested readers may see [10] [12] [15] [20] [21] [28] [33] [34] [40] [42] [45] [46] [47] [50] [53] [54] and the references therein.”
• Maximum principles for a fully nonlinear fractional order equation and symmetry of solutions (2016, methodology): “ction 4, we derive Theorem 7. For more articles concerning the method of moving planes for nonlocal equations and for integral equations, please see [FL] [Ha] [HLZ] [HWY] [Lei] [LLM] [LZ] [LZ1] [LZ2] [MC] [MZ] and the references therein. 2 VariousMaximum Principles Let Fα(u(x)) = Cn,α PV Z Rn G(u(x)”
• Liouville type theorems for nonlinear elliptic equations and systems involving fractional Laplacian in the half space (2015, methodology): “We can deduce the following result from Theorem 1 in [23] and regularity results Theorems 2.”
• A direct method of moving planes for the fractional Laplacian (2014, unknown): “local elliptic equations. For more articles concerning the method of moving planes for nonlocal equations, mainly for integral equations, please see [FL] [Ha] [HLZ] [HWY] [Lei] [LLM] [LZ] [LZ1] [LZ2] [MC] [MZ] and the references therein. 2 Various Maximum Principles 2.1 A Maximum Principle for Anti-”
• Liouville type theorems for integral equations and integral systems (2013, background): “For example, in [22], the authors studied integral system (2) with f (u, v) = v p, g(u, v) = uq .”
• Maximum principles for the fractional p-Laplacian and symmetry of solutions (2017, methodology): “nd 4 respectively. For more articles concerning the method of moving planes for nonlocal equations and for integral equations, please see [CLv] [FL] [Ha] [HLZ] [HWY] [Lei] [LL] [LLM] [LZ] [LZ1] [LZ2] [MC] [MZ] and the references therein. 2 Various Maximum Principles and a Boundary Estimate Let (−△)s”
• Radial symmetry and monotonicity for an integral equation (2008, methodology): “Recently, it was first observed by Chen, Li and Ou [4,5,12] that instead of the maximum principle, one can use a Hardy–Littlewood–Sobolev (HLS) type inequality to obtain the radial symmetry and monotonicity of nonnegative solutions of (systems of) elliptic equations of Yamabe type.”