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- Title
Monotonicity and Liouville type theorems of solutions to fully nonlinear fractional problems in the half space.
- Authors
Cheng, Tingzhi; Xu, Xianghui
- Abstract
This paper mainly deals with the monotonicity and Liouville type theorems of nonnegative solutions for a class of fully nonlinear fractional equations in half-space. Compared with serial works in [9,14,20], the restrictions on the monotonicity of nonlinear terms and the decay assumption on solutions are not necessary here. Moreover, the monotonicity result of nonnegative bounded solutions for corresponding cooperative systems is also derived. Specifically, we establish some new types of maximum principles for fully nonlinear fractional equations and systems in unbounded domains, which will play crucial roles in carrying on the method of moving planes.
- Subjects
LIOUVILLE'S theorem; NONLINEAR equations; MAXIMUM principles (Mathematics); NONLINEAR operators
- Publication
Discrete & Continuous Dynamical Systems: Series A, 2024, Vol 44, Issue 7, p1
- ISSN
1078-0947
- Publication type
Article
- DOI
10.3934/dcds.2024020