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SOME EXISTENCE AND UNIQUENESS RESULTS FOR INFINITY LAPLACE EQUATIONS ON INFINITE GRAPHS

delete2026-03-01
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PRE
AI
H
Han, Fengwen
W
Wang, Tao *
DOI：10.3934/cpaa.2026051delete
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Abstract

Abstract

En 中文
We study the Dirichlet problem of the following discrete infinity Laplace equation on unbounded subgraphs triangle infinity u(x) := inf u(y) + sup y similar to xy similar to x u(y)-2u(x) = f (x). For the homogeneous case (f = 0), the existence and uniqueness of sublinear solutions are established. This result is applied to prove the existence and uniqueness of sublinear solutions for the homogeneous (normalized) infinity Laplace equations on unbounded Euclidean domains. Uniqueness is also shown for the case f >= 0 on trees.
Keywords:
Infinity Laplacian
infinite graphs
unbounded domains
sublinear solutions
existence and uniqueness results

Journal

C
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
IF:
0.9
Papers:
88
Citations:
0

Organization

P
peking university
Scholars:
11.5W
Papers: 8.6W
Citations: 146
H
henan university
Scholars:
2.2W
Papers: 1.3W
Citations: 20
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