Nonnegative or sign-changing solutions to semilinear elliptic equations on metric graphs with positive potential are only the trivial zero solution under suitable volume growth conditions.
Mugnolo, Semigroup Methods for Evolution Equations on Networks, Springer
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Nonexistence results for semilinear elliptic equations on metric graphs
Nonnegative or sign-changing solutions to semilinear elliptic equations on metric graphs with positive potential are only the trivial zero solution under suitable volume growth conditions.