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The unit condition and global existence for a class of nonlinear Klein- Gordon equations. (English) Zbl 0781.35062
Summary: Global existence for a special class of nonlinear Klein-Gordon equations in two space dimensions is proved. In particular it is shown that, for small initial data, the equation $\partial\sb{tt} u-\Delta u+ u= u\sp 2$ has a global solution.

##### MSC:
 35Q53 KdV-like (Korteweg-de Vries) equations 35L15 Second order hyperbolic equations, initial value problems 35B65 Smoothness and regularity of solutions of PDE
##### Keywords:
two space dimensions; small initial data
Full Text:
##### References:
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