Strauss, Walter A.; Tsutaya, Kimitoshi Existence and blow up of small amplitude nonlinear waves with a negative potential. (English) Zbl 0948.35084 Discrete Contin. Dyn. Syst. 3, No. 2, 175-188 (1997). 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. Cited in 15 Documents 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 Keywords:three space dimensions; zero mass together with a negative potential PDFBibTeX XMLCite \textit{W. A. Strauss} and \textit{K. Tsutaya}, Discrete Contin. Dyn. Syst. 3, No. 2, 175--188 (1997; Zbl 0948.35084) Full Text: DOI