# American Institute of Mathematical Sciences

April  1997, 3(2): 175-188. doi: 10.3934/dcds.1997.3.175

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

 1 Department of Mathematics and LCDS, Brown University, Providence, RI 02912, United States 2 Department of Mathematics, Brown University, Providence, R.I. 02912, United States

Received  November 1996 Published  January 1997

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.
Citation: Walter A. Strauss, Kimitoshi Tsutaya. Existence and blow up of small amplitude nonlinear waves with a negative potential. Discrete & Continuous Dynamical Systems, 1997, 3 (2) : 175-188. doi: 10.3934/dcds.1997.3.175
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