The unique continuation property for a nonlinear equation on trees

In this paper we study the game $p-$Laplacian on a tree, that is, $u(x)=\fracα2\left\{\max_{y\in §(x)}u(y) + \min_{y\in §(x)}u(y)\right\} + \fracβ{m}\sum_{y\in §(x)} u(y),$ here $x$ is a vertex of the tree and $S(x)$ is the set of successors of $x$. We study the family of the subsets of the tree that enjoy the unique continuation property, that is, subsets $U$ such that $u\mid_U=0$ implies $u \equiv 0$.

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