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

@inproceedings{Hakl2012PUBI,
  title={PU BL IC On the open problems connected to the results of Lazer and Solimini},
  author={Robert Hakl and Manuel Zamora},
  year={2012}
}
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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Referenced Papers

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Showing 1-8 of 8 references

On periodic solutions of nonlinear differential equations with singularities

  • A. C. Lazer, S. Solimini
  • Proc. Amer. Math. Soc
  • 1987
Highly Influential
8 Excerpts

Periodic solutions of singular second order differential equations: Upper and lower functions

  • R. Hakl, P. J. Torres, M. Zamora
  • Nonlinear Anal
  • 2011
2 Excerpts

Solvability of nonlinear singular problems for ordinary differential equations , Contemp

  • S. Staněk I. Rach̊unková, M. Tvrdý
  • Math . Appl .
  • 2008

Vrkoč, Existence of nonnegative and nonpositive solutions for second order periodic boundary value problems

  • I. Rach̊unková, I. M. Tvrdý
  • J. Differential Equations
  • 2001
2 Excerpts

Periodic solutions of some Liénard equations with singularities

  • P. Habets, L. Sanchez
  • Proc. Amer. Math. Soc
  • 1990
2 Excerpts

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