INFINITELY MANY PERIODIC SOLUTIONS FOR THE EQUATION:

@inproceedings{Tanaka2010INFINITELYMP,
  title={INFINITELY MANY PERIODIC SOLUTIONS FOR THE EQUATION:},
  author={Kazuyoshi Tanaka},
  year={2010}
}
Existence of forced vibrations of nonlinear wave equation: utt uxx ± \u\"~lu = f(x, t), (x, t) € (0, 7l) X R, u(0, t) = u(tt, t) = 0, teR, u(x, t + 2n) = u(x,t), (x, t) € (0,7r) x R, is considered. For all p € (1, oo) and f(x, t) £ z/p+1'/p, existence of infinitely many periodic solutions is proved. This improves the results of the author [29, 30]. We use variational methods to show the existence result. Minimax arguments and energy estimates for the corresponding functional play an essential… CONTINUE READING

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