Unbounded Solutions of Almost Periodically Forced Pendulum-Type Equations

In this paper, we prove that the forced pendulum-type equation x*Gx(x,t)=p(t), where G(x,t) C 1 (R 2) with 1-periodicity in x satisfies the conditions: sup(x,t)R2|Gx(x,t)|>* and limsupt{supxRGt(x,t)t}=0, possesses infinitely many unbounded solutions on a cylinder S 1R for any almost periodic function p(t) with nonvanishing mean value.