A5050350701- Advanced Mathematical Modeling in Engineering
- Nonlinear Partial Differential Equations
- Nonlinear Differential Equations Analysis
- Advanced Mathematical Physics Problems
- Stability and Controllability of Differential Equations
- Differential Equations and Numerical Methods
- Numerical methods in inverse problems
- advanced mathematical theories
- Nonlinear Photonic Systems
- Spectral Theory in Mathematical Physics
- Differential Equations and Boundary Problems
- Cold Atom Physics and Bose-Einstein Condensates
- Fractional Differential Equations Solutions
University of Science and Technology Beijing
2014-2024
In this paper, we consider fractional equations involving the logarithmic Laplacian with indefinite nonlinearities: [Formula: see text] where represents a Lipschitz coercive epigraph. Our investigation begins by establishing boundary estimate for antisymmetric functions and demonstrating monotonicity of bounded positive solutions in epigraphs, via direct method moving planes. Subsequently, present Liouville-type theorem nonlocal problem.
In this paper, we extend the direct method of moving planes to tempered fractional Laplacian equations. To carry out method, a narrow region principle and decay at infinity lemma are established firstly. Moreover, boundary estimate is also discussed. Then, obtain radial symmetry result for positive solutions equations both in unit ball on whole space.