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Sharp conditions of global existence for nonlinear Klein-Gordon equations. (Chinese. English summary) Zbl 1117.35324

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.

MSC:

35L70 Second-order nonlinear hyperbolic equations
35B40 Asymptotic behavior of solutions to PDEs
35L15 Initial value problems for second-order hyperbolic equations
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