A nonlinear periodic system with nonsmooth potential of indefinite sign

Michael E. Filippakis; Nikolaos S. Papageorgiou

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 3, page 205-213
  • ISSN: 0044-8753

Abstract

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In this paper we consider a nonlinear periodic system driven by the vector ordinary p -Laplacian and having a nonsmooth locally Lipschitz potential, which is positively homogeneous. Using a variational approach which exploits the homogeneity of the potential, we establish the existence of a nonconstant solution.

How to cite

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Filippakis, Michael E., and Papageorgiou, Nikolaos S.. "A nonlinear periodic system with nonsmooth potential of indefinite sign." Archivum Mathematicum 042.3 (2006): 205-213. <http://eudml.org/doc/249815>.

@article{Filippakis2006,
abstract = {In this paper we consider a nonlinear periodic system driven by the vector ordinary $p$-Laplacian and having a nonsmooth locally Lipschitz potential, which is positively homogeneous. Using a variational approach which exploits the homogeneity of the potential, we establish the existence of a nonconstant solution.},
author = {Filippakis, Michael E., Papageorgiou, Nikolaos S.},
journal = {Archivum Mathematicum},
keywords = {locally Lipschitz function; generalized subdifferential; $p$-Laplacian; homogeneous function; variational method; Poincare-Wirtinger inequality; potential indefinite in sign; locally Lipschitz function; generalized subdifferential; -Laplacian; homogeneous function; variational method},
language = {eng},
number = {3},
pages = {205-213},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A nonlinear periodic system with nonsmooth potential of indefinite sign},
url = {http://eudml.org/doc/249815},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Filippakis, Michael E.
AU - Papageorgiou, Nikolaos S.
TI - A nonlinear periodic system with nonsmooth potential of indefinite sign
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 3
SP - 205
EP - 213
AB - In this paper we consider a nonlinear periodic system driven by the vector ordinary $p$-Laplacian and having a nonsmooth locally Lipschitz potential, which is positively homogeneous. Using a variational approach which exploits the homogeneity of the potential, we establish the existence of a nonconstant solution.
LA - eng
KW - locally Lipschitz function; generalized subdifferential; $p$-Laplacian; homogeneous function; variational method; Poincare-Wirtinger inequality; potential indefinite in sign; locally Lipschitz function; generalized subdifferential; -Laplacian; homogeneous function; variational method
UR - http://eudml.org/doc/249815
ER -

References

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