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| Volume 11, Number 1, April 2010, pp. 115-136 | ||||||
| N. S. Papageorgiou, E. M. Rocha and V. Staicu | ||||||
| Key words: | ||||||
| Locally Lipschitz potential, generalized subdifferential, nonlinear maximum principle, three nontrivial solutions, nonlinear regularity theory, PS-condition, linking sets, minimax principle, second deformation theorem | ||||||
| Mathematices Subject Classification: 35J20, 35J25, 35J60, 35J70 | ||||||
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| Abstract: | |||
| We consider a nonlinear elliptic problem with a nonsmooth potential function. The nonlinear differential operator includes as special case the $p-$Laplacian. Using a variational approach based on nonsmooth critical point theory, we show the existence of at least three nontrivial smooth solutions. Two of them have constant sign (one is positive and the other is negative). | |||
| On the existence of three nontrivial smooth solutions for nonlinear elliptic equations |
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