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Existence and blow up of small amplitude nonlinear waves with a negative potential. (English) Zbl 0948.35084

Summary: 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.

MSC:

35L70 Second-order nonlinear hyperbolic equations
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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