Multiple Solutions for Nonlinear Periodic Problems

Kyritsi, Sophia Th. ; Papageorgiou, Nikolaos S.

Canadian mathematical bulletin, Tome 56 (2013) no. 2, pp. 366-377

Résumé

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).

Détail

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

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