Geodesic
Periodic solutions for systems with nonsmooth and partially coercive potential
Archivum mathematicum, Tome 42 (2006) no. 3, pp. 225-232.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.).
Classification : 34A60, 34B15, 34C25, 47J30, 47N20
Keywords: locally linking Lipschitz function; generalized subdifferential; nonsmooth critical point theory; nonsmooth Palais-Smale condition; $p$-Laplacian; periodic system 
@article{ARM_2006__42_3_a2,
     author = {Filippakis, Michael E.},
     title = {Periodic solutions for systems with nonsmooth and partially coercive potential},
     journal = {Archivum mathematicum},
     pages = {225--232},
     publisher = {mathdoc},
     volume = {42},
     number = {3},
     year = {2006},
     mrnumber = {2260380},
     zbl = {1164.34319},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2006__42_3_a2/}
}
TY  - JOUR
AU  - Filippakis, Michael E.
TI  - Periodic solutions for systems with nonsmooth and partially coercive potential
JO  - Archivum mathematicum
PY  - 2006
SP  - 225
EP  - 232
VL  - 42
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ARM_2006__42_3_a2/
LA  - en
ID  - ARM_2006__42_3_a2
ER  - 
%0 Journal Article
%A Filippakis, Michael E.
%T Periodic solutions for systems with nonsmooth and partially coercive potential
%J Archivum mathematicum
%D 2006
%P 225-232
%V 42
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ARM_2006__42_3_a2/
%G en
%F ARM_2006__42_3_a2
Filippakis, Michael E. Periodic solutions for systems with nonsmooth and partially coercive potential. Archivum mathematicum, Tome 42 (2006) no. 3, pp. 225-232. http://geodesic.mathdoc.fr/item/ARM_2006__42_3_a2/