Multiple solutions for nonlinear periodic problems with discontinuities

Nikolaos S. Papageorgiou; Nikolaos Yannakakis

Archivum Mathematicum (2002)

  • Volume: 038, Issue: 3, page 171-182
  • ISSN: 0044-8753

Abstract

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In this paper we consider a periodic problem driven by the one dimensional p -Laplacian and with a discontinuous right hand side. We pass to a multivalued problem, by filling in the gaps at the discontinuity points. Then for the multivalued problem, using the nonsmooth critical point theory, we establish the existence of at least three distinct periodic solutions.

How to cite

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Papageorgiou, Nikolaos S., and Yannakakis, Nikolaos. "Multiple solutions for nonlinear periodic problems with discontinuities." Archivum Mathematicum 038.3 (2002): 171-182. <http://eudml.org/doc/248941>.

@article{Papageorgiou2002,
abstract = {In this paper we consider a periodic problem driven by the one dimensional $p$-Laplacian and with a discontinuous right hand side. We pass to a multivalued problem, by filling in the gaps at the discontinuity points. Then for the multivalued problem, using the nonsmooth critical point theory, we establish the existence of at least three distinct periodic solutions.},
author = {Papageorgiou, Nikolaos S., Yannakakis, Nikolaos},
journal = {Archivum Mathematicum},
keywords = {multiple solutions; periodic problem; one-dimensional $p$-Laplacian; discontinuous vector field; nonsmooth Palais-Smale condition; locally Lipschitz function; generalized subdifferential; critical point; Saddle Point Theorem; Ekeland variational principle; multiple solutions; periodic problem; one-dimensional -Laplacian; discontinuous vector field; nonsmooth Palais-Smale condition; locally Lipschitz function; generalized subdifferential; critical point},
language = {eng},
number = {3},
pages = {171-182},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Multiple solutions for nonlinear periodic problems with discontinuities},
url = {http://eudml.org/doc/248941},
volume = {038},
year = {2002},
}

TY - JOUR
AU - Papageorgiou, Nikolaos S.
AU - Yannakakis, Nikolaos
TI - Multiple solutions for nonlinear periodic problems with discontinuities
JO - Archivum Mathematicum
PY - 2002
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 038
IS - 3
SP - 171
EP - 182
AB - In this paper we consider a periodic problem driven by the one dimensional $p$-Laplacian and with a discontinuous right hand side. We pass to a multivalued problem, by filling in the gaps at the discontinuity points. Then for the multivalued problem, using the nonsmooth critical point theory, we establish the existence of at least three distinct periodic solutions.
LA - eng
KW - multiple solutions; periodic problem; one-dimensional $p$-Laplacian; discontinuous vector field; nonsmooth Palais-Smale condition; locally Lipschitz function; generalized subdifferential; critical point; Saddle Point Theorem; Ekeland variational principle; multiple solutions; periodic problem; one-dimensional -Laplacian; discontinuous vector field; nonsmooth Palais-Smale condition; locally Lipschitz function; generalized subdifferential; critical point
UR - http://eudml.org/doc/248941
ER -

References

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