Maximum principles for a fully nonlinear nonlocal equation on unbounded domains
Maximum principles for a fully nonlinear nonlocal equation on unbounded domains
In this paper, we study equations involving fully nonlinear nonlocal operators \begin{document}$ \mathcal {F}_{\alpha}(u(x)) = C_{n, \alpha}P.V.\int_{ \mathbb R^n}\frac{G(u(x)-u(z))}{|x-z|^{n+\alpha}}dz = f(u(x)), \; \; \; x\in \mathbb R^n. $\end{document} We shall establish a maximum principle for anti-symmetric functions on any half space, and obtain key ingredients for proving the symmetry and …