RESUMEN

The existence of 2Π-periodic solutions to the equations x'''+ax''+g (t, x’) +cx=p(t) is proved, under certain non-resonance condition on the non-linear function g(t,y) . Here a, c are constants but the case where a,c are not necessarily constants is also discussed, subject to some rather special non-resonance conditions on g. The uniqueness of the solutions is also examined.

In this paper, it is proved that the "null condition" implies the global existence of the solutions to Cauchy problem wave equations, where the nonlinear term contains the unknown function itself, for small initial data in three four space dimensions