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.
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Nonexistence of all very weak solutions to semilinear parabolic and hyperbolic inequalities on metric graphs under weighted space-time volume growth conditions on the potential, via a new pseudo-metric and coupled/separated test functions.
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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.
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Nonexistence Results for Semilinear Parabolic and Hyperbolic Equations on Metric Graphs
Nonexistence of all very weak solutions to semilinear parabolic and hyperbolic inequalities on metric graphs under weighted space-time volume growth conditions on the potential, via a new pseudo-metric and coupled/separated test functions.