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Differential and Difference Equations with Applications pp 83–98Cite as

Periodic Solutions of Differential and Difference Systems with Pendulum-Type Nonlinearities: Variational Approaches

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 47))

Abstract

We survey some recent results on the use of variational methods in proving the existence and multiplicity of periodic solutions of systems of differential equations of the type

$$\displaystyle{(\phi (q^{\prime}))^{\prime} = \nabla _{q}F(t,q) + h(t)}$$

or systems of difference equations of the type

$$\displaystyle{\varDelta (\phi (\varDelta q(n - 1))) = \nabla _{q}F(n,q) + h(n)\quad (n \in \mathbb{Z})}$$

when ϕ belongs to a class of suitable homeomorphisms between an open ball and the whole space and F is periodic in the components of q.

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Authors and Affiliations

  1. Institut de Recherche en Mathématique et Physique, Université Catholique de Louvain, chemin du cyclotron, 2, B-1348, Louvain-la-Neuve, Belgium

    Jean Mawhin

Authors
  1. Jean Mawhin
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Correspondence to Jean Mawhin .

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Editors and Affiliations

  1. Departamento de Ciências Exactas e Naturais, Academia Militar, Amadora, Portugal

    Sandra Pinelas

  2. University of Zürich Institute of Mathematics, Zürich, Switzerland

    Michel Chipot

  3. Masaryk University Dept. Mathematics, Brno, Czech Republic

    Zuzana Dosla

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Mawhin, J. (2013). Periodic Solutions of Differential and Difference Systems with Pendulum-Type Nonlinearities: Variational Approaches. In: Pinelas, S., Chipot, M., Dosla, Z. (eds) Differential and Difference Equations with Applications. Springer Proceedings in Mathematics & Statistics, vol 47. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7333-6_7

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