# American Institute of Mathematical Sciences

July  2009, 8(4): 1421-1437. doi: 10.3934/cpaa.2009.8.1421

## Three nontrivial solutions for periodic problems with the $p$-Laplacian and a $p$-superlinear nonlinearity

 1 Jagiellonian University, Institute of Computer Science, ul. Nawojki 11, 30072 Kraków 2 Department of Mathematics, National Technical University, Zografou Campus, Athens 15780

Received  May 2008 Revised  October 2008 Published  March 2009

We consider a nonlinear periodic problem driven by the scalar $p$-Laplacian and a nonlinearity that exhibits a $p$-superlinear growth near $\pm\infty$, but need not satisfy the Ambrosetti-Rabinowitz condition. Using minimax methods, truncations techniques and Morse theory, we show that the problem has at least three nontrivial solutions, two of which are of fixed sign.
Citation: Leszek Gasiński, Nikolaos S. Papageorgiou. Three nontrivial solutions for periodic problems with the $p$-Laplacian and a $p$-superlinear nonlinearity. Communications on Pure & Applied Analysis, 2009, 8 (4) : 1421-1437. doi: 10.3934/cpaa.2009.8.1421
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