Geodesic
Existence of Positive Solutions for Nonlinear Noncoercive Hemivariational Inequalities
Canadian mathematical bulletin, Tome 50 (2007) no. 3, pp. 356-364

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DOI

In this paper we investigate the existence of positive solutions for nonlinear elliptic problems driven by the $p$ -Laplacian with a nonsmooth potential (hemivariational inequality). Under asymptotic conditions that make the Euler functional indefinite and incorporate in our framework the asymptotically linear problems, using a variational approach based on nonsmooth critical point theory, we obtain positive smooth solutions. Our analysis also leads naturally to multiplicity results.
DOI : 10.4153/CMB-2007-034-6
Mots-clés : 35J20, 35J60, 35J85, p-Laplacian, locally Lipschitz potential, nonsmooth critical point theory, principal eigenvalue, positive solutions, nonsmooth Mountain Pass Theorem 
Filippakis, Michael E.; Papageorgiou, Nikolaos S. Existence of Positive Solutions for Nonlinear Noncoercive Hemivariational Inequalities. Canadian mathematical bulletin, Tome 50 (2007) no. 3, pp. 356-364. doi: 10.4153/CMB-2007-034-6
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     author = {Filippakis, Michael E. and Papageorgiou, Nikolaos S.},
     title = {Existence of {Positive} {Solutions} for {Nonlinear} {Noncoercive} {Hemivariational} {Inequalities}},
     journal = {Canadian mathematical bulletin},
     pages = {356--364},
     year = {2007},
     volume = {50},
     number = {3},
     doi = {10.4153/CMB-2007-034-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-034-6/}
}
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