PU BL IC On the open problems connected to the results of Lazer and Solimini

  title={PU BL IC On the open problems connected to the results of Lazer and Solimini},
  author={Robert Hakl and Manuel Zamora},
A well-known theorem proved by A. C. Lazer and S. Solimini claims that the singular equation u′′ + 1 uλ = h(t), λ > 0, has a periodic solution if and only if the mean value of the continuous external force is positive. In this paper, we show that this result cannot be extended to the case when h is an integrable function, unless the additional assumptions are introduced. In addition, for each p ≥ 1 and h integrable function in the p-th power, we give a sharp condition guaranteeing the existence… CONTINUE READING

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