TY - JOUR
T1 - A direct method of moving planes for fully nonlinear nonlocal operators and applications
AU - Guo, Yuxia
AU - Peng, Shaolong
N1 - Publisher Copyright:
© 2021 American Institute of Mathematical Sciences. All rights reserved.
PY - 2021/6
Y1 - 2021/6
N2 - In this paper, we are concerned with the following generalized fully nonlinear nonlocal operators: Fs;m(u(x)) = cN;sm N2 +sP:V: Z RN G(u(x) - u(y)) lx - yl N2 +s KN2 +s(mlx-yl)dy+m2su(x); where s 2 (0; 1) and mass m > 0. By establishing various maximal principle and using the direct method of moving plane, we prove the monotonicity, symmetry and uniqueness for solutions to fully nonlinear nonlocal equation in unit ball, RN, RN+ and a coercive epigraph domain in RN respectively.
AB - In this paper, we are concerned with the following generalized fully nonlinear nonlocal operators: Fs;m(u(x)) = cN;sm N2 +sP:V: Z RN G(u(x) - u(y)) lx - yl N2 +s KN2 +s(mlx-yl)dy+m2su(x); where s 2 (0; 1) and mass m > 0. By establishing various maximal principle and using the direct method of moving plane, we prove the monotonicity, symmetry and uniqueness for solutions to fully nonlinear nonlocal equation in unit ball, RN, RN+ and a coercive epigraph domain in RN respectively.
KW - Direct methods of moving planes
KW - Fully nonlinear nonlocal operators
KW - Liouville theorem
KW - Maximal principle
KW - Symmetry and Monotonicity
UR - https://www.scopus.com/pages/publications/85108851931
U2 - 10.3934/DCDSS.2020462
DO - 10.3934/DCDSS.2020462
M3 - 文章
AN - SCOPUS:85108851931
SN - 1937-1632
VL - 14
SP - 1871
EP - 1897
JO - Discrete and Continuous Dynamical Systems - Series S
JF - Discrete and Continuous Dynamical Systems - Series S
IS - 6
ER -