Minimax Theory and its Applications 02 (2017), No. 1, 069--078
Copyright Heldermann Verlag 2017
Multiplicity Results for some Quasilinear Differential Systems with Periodic Nonlinearities
Petru Jebelean
Dept. of Mathematics, West University of Timisoara, 4 Blvd. V. Pârvan, 300223 Timisoara, Romania
petru.jebelean@e-uvt.ro
Jean Mawhin
Dép. de Mathématique, Université Catholique de Louvain, 2 Chemin du Cyclotron, 1348 Louvain-la-Neuve, Belgique
jean.mawhin@uclouvain.be
Calin Serban
Dept. of Mathematics, West University of Timisoara, 4 Blvd. V. Pârvan, 300223 Timisoara, Romania
cserban2005@yahoo.com
[Abstract-pdf]
\newcommand{\RN}{{\mathbb R}^N} A multiplicity result for periodic problems of the form $$ -(\psi(u'))' = \nabla_u V(t,u) + e(t), \;\; u(0) = u(T),\; u'(0) = u'(T), $$ when $\psi : \RN \to \RN$ belongs to a suitable class of homeomorphisms, $V$ is $T_i$-periodic in each component $u_i$ of $u \in \RN$, and $e$ has mean value zero on $[0,T]$ is proved, and applied, by a modification technique, to obtain the same multiplicity for the solutions of the relativistic system $$ -\left(\frac{u'}{\sqrt{1 - |u'|^2}}\right)' = \nabla_u V(t,u) + e(t), \;\; u(0) = u(T),\; u'(0) = u'(T). $$
Keywords: Periodic solutions, periodic nonlinearities, relativistic pendulum systems.
MSC: 34C25; 35J25, 35J65
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