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arXiv · 2604.03736

Nonexistence results for semilinear elliptic equations on metric graphs

Yang Liu·Yong Lin·Haohang Zhang
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Abstract

In this paper, we study the nonexistence of solutions to semilinear elliptic equations with a positive potential on metric graphs. In particular, the Laplacian under consideration is of a special type, related to both the vertices and edges of metric graphs. We construct a modified distance function, introduce appropriate test functions, and establish the nonexistence of global solutions under suitable volume growth conditions imposed on the potential. More precisely, the nonnegative solutions or sign-changing solutions to the equations are the trivial zero solutions.

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Yang Liu, Yong Lin, Haohang Zhang. 2026-04-04. Nonexistence results for semilinear elliptic equations on metric graphs. https://arxiv.org/abs/2604.03736

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