Geodesic
Multiple Solutions for Nonlinear Periodic Problems
Canadian mathematical bulletin, Tome 56 (2013) no. 2, pp. 366-377

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DOI

We consider a nonlinear periodic problem driven by a nonlinear nonhomogeneous differential operator and a Carathéodory reaction term $f\left( t,\,x \right)$ that exhibits a $\left( p\,-\,1 \right)$ -superlinear growth in $x\,\in \,\mathbb{R}$ near $\pm \infty $ and near zero. A special case of the differential operator is the scalar $p$ -Laplacian. Using a combination of variational methods based on the critical point theory with Morse theory (critical groups), we show that the problem has three nontrivial solutions, two of which have constant sign (one positive, the other negative).
DOI : 10.4153/CMB-2011-154-5
Mots-clés : 34B15, 34B18, 34C25, 58E05, C-condition, mountain pass theorem, critical groups, strong deformation retract, contractible space, homotopy invariance 
Kyritsi, Sophia Th.; Papageorgiou, Nikolaos S. Multiple Solutions for Nonlinear Periodic Problems. Canadian mathematical bulletin, Tome 56 (2013) no. 2, pp. 366-377. doi: 10.4153/CMB-2011-154-5
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     title = {Multiple {Solutions} for {Nonlinear} {Periodic} {Problems}},
     journal = {Canadian mathematical bulletin},
     pages = {366--377},
     year = {2013},
     volume = {56},
     number = {2},
     doi = {10.4153/CMB-2011-154-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-154-5/}
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