MMN-5000
Existence of super-solutions of a discrete equation of Wolff type
Hong Huang; Tiantian Zhou;Abstract
In this paper, we are concerned with the
Wolff-type equation
$$
u_i=\int_0^\infty\left(\frac{\sum_{j \in \mathbb{Z}^n,|j-i|0 \quad \textrm{for} \ \ i \in \mathbb{Z}^n,
$$
where $n \geq 1$, $\min\{\beta, \gamma, p\}>0$ and $\beta\gamma
< n$. Such an equation is related to the study in the theory of
nonlinear PDEs and mathematical physics. Here we study the existence of positive
super-solutions and obtain the critical exponent of the Serrin type.
Vol. 27 (2026), No. 1, pp. 209-217