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, Parabolic theory of the discrete p-Laplace operator, Nonlinear Anal
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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.