Gan, Zaihui; Zhang, Jian Sharp conditions of global existence for nonlinear Klein-Gordon equations. (Chinese. English summary) Zbl 1117.35324 Acta Math. Sin. 48, No. 2, 311-318 (2005). Summary: This paper is concerned with the Cauchy problem for a class of nonlinear Klein-Gordon equations with several competing potential functions. In terms of the characteristics of the ground state, the sharp conditions for blowing up and global existence are derived out by applying the potential well argument and the concavity method. And the question that how small the initial data are, the global solutions exist is answered. Cited in 3 Documents MSC: 35L70 Second-order nonlinear hyperbolic equations 35B40 Asymptotic behavior of solutions to PDEs 35L15 Initial value problems for second-order hyperbolic equations Keywords:nonlinear Klein-Gordon equation; sharp condition; global existence; potential well argument; concavity method PDFBibTeX XMLCite \textit{Z. Gan} and \textit{J. Zhang}, Acta Math. Sin. 48, No. 2, 311--318 (2005; Zbl 1117.35324)