期刊
ADVANCES IN MATHEMATICS
卷 361, 期 -, 页码 -出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2019.106933
关键词
The fractional p-Laplacian; Narrow region principle; Sliding methods; Monotonicity of solutions
类别
资金
- National Natural Science Foundation of China [11571233, 11831003, 11701207]
In this paper, we develop a sliding method for the fractional p-Laplacian. We first obtain the key ingredient needed in the sliding method in a bounded domain the narrow region principle. Then using nonlinear equations involving the fractional p-Laplacian in both bounded domains and in the whole space, we illustrate how this new sliding method can be employed to obtain monotonicity of solutions. During these processes, we introduce a new idea estimating the singular integrals defining the fractional p-Laplacian along a sequence of approximate maximum points. We believe that the new ideas and methods employed here can be conveniently applied to study a variety of nonlocal problems with more general operators and more general nonlinearities. (C) 2019 Elsevier Inc. All rights reserved.
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