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Existence and blow up of small amplitude nonlinear waves with a negative potential

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  • Consider a nonlinear wave equation in three space dimensions with zero mass together with a negative potential. If the potential is sufficiently short-range, then it does not alter the global existence of small-amplitude solutions. On the other hand, if the potential is sufficiently large, it will force some solutions to blow up in a finite time.
    Mathematics Subject Classification: 35L70, 35B35.

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