Geodesic
A nonlinear periodic system with nonsmooth potential of indefinite sign
Archivum mathematicum, Tome 42 (2006) no. 3, pp. 205-213.

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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.
Classification : 34A60, 34B15, 34C25, 47J30, 47N20
Keywords: locally Lipschitz function; generalized subdifferential; $p$-Laplacian; homogeneous function; variational method; Poincare-Wirtinger inequality; potential indefinite in sign 
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     author = {Filippakis, Michael E. and Papageorgiou, Nikolaos S.},
     title = {A nonlinear periodic system with nonsmooth potential of indefinite sign},
     journal = {Archivum mathematicum},
     pages = {205--213},
     publisher = {mathdoc},
     volume = {42},
     number = {3},
     year = {2006},
     mrnumber = {2260378},
     zbl = {1164.34404},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2006__42_3_a0/}
}
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Filippakis, Michael E.; Papageorgiou, Nikolaos S. A nonlinear periodic system with nonsmooth potential of indefinite sign. Archivum mathematicum, Tome 42 (2006) no. 3, pp. 205-213. http://geodesic.mathdoc.fr/item/ARM_2006__42_3_a0/