Periodic solutions for systems with nonsmooth and partially coercive potential

Michael E. Filippakis

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 3, page 225-232
  • ISSN: 0044-8753

Abstract

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In this paper we consider nonlinear periodic systems driven by the one-dimensional p -Laplacian and having a nonsmooth locally Lipschitz potential. Using a variational approach based on the nonsmooth Critical Point Theory, we establish the existence of a solution. We also prove a multiplicity result based on a nonsmooth extension of the result of Brezis-Nirenberg (Brezis, H., Nirenberg, L., Remarks on finding critical points, Comm. Pure Appl. Math. 44 (1991), 939–963.) due to Kandilakis-Kourogenis-Papageorgiou (Kandilakis, D., Kourogenis, N., Papageorgiou, N., Two nontrivial critical point for nosmooth functional via local linking and applications, J. Global Optim., to appear.).

How to cite

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Filippakis, Michael E.. "Periodic solutions for systems with nonsmooth and partially coercive potential." Archivum Mathematicum 042.3 (2006): 225-232. <http://eudml.org/doc/249779>.

@article{Filippakis2006,
abstract = {In this paper we consider nonlinear periodic systems driven by the one-dimensional $p$-Laplacian and having a nonsmooth locally Lipschitz potential. Using a variational approach based on the nonsmooth Critical Point Theory, we establish the existence of a solution. We also prove a multiplicity result based on a nonsmooth extension of the result of Brezis-Nirenberg (Brezis, H., Nirenberg, L., Remarks on finding critical points, Comm. Pure Appl. Math. 44 (1991), 939–963.) due to Kandilakis-Kourogenis-Papageorgiou (Kandilakis, D., Kourogenis, N., Papageorgiou, N., Two nontrivial critical point for nosmooth functional via local linking and applications, J. Global Optim., to appear.).},
author = {Filippakis, Michael E.},
journal = {Archivum Mathematicum},
keywords = {locally linking Lipschitz function; generalized subdifferential; nonsmooth critical point theory; nonsmooth Palais-Smale condition; $p$-Laplacian; periodic system; locally linking Lipschitz function; generalized subdifferential; nonsmooth critical point theory},
language = {eng},
number = {3},
pages = {225-232},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Periodic solutions for systems with nonsmooth and partially coercive potential},
url = {http://eudml.org/doc/249779},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Filippakis, Michael E.
TI - Periodic solutions for systems with nonsmooth and partially coercive potential
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 3
SP - 225
EP - 232
AB - In this paper we consider nonlinear periodic systems driven by the one-dimensional $p$-Laplacian and having a nonsmooth locally Lipschitz potential. Using a variational approach based on the nonsmooth Critical Point Theory, we establish the existence of a solution. We also prove a multiplicity result based on a nonsmooth extension of the result of Brezis-Nirenberg (Brezis, H., Nirenberg, L., Remarks on finding critical points, Comm. Pure Appl. Math. 44 (1991), 939–963.) due to Kandilakis-Kourogenis-Papageorgiou (Kandilakis, D., Kourogenis, N., Papageorgiou, N., Two nontrivial critical point for nosmooth functional via local linking and applications, J. Global Optim., to appear.).
LA - eng
KW - locally linking Lipschitz function; generalized subdifferential; nonsmooth critical point theory; nonsmooth Palais-Smale condition; $p$-Laplacian; periodic system; locally linking Lipschitz function; generalized subdifferential; nonsmooth critical point theory
UR - http://eudml.org/doc/249779
ER -

References

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