Ordinary Differential Equations

  • Dumitru Motreanu
  • Viorica Venera Motreanu
  • Nikolaos Papageorgiou
Chapter

Abstract

This chapter examines the existence and multiplicity of periodic solutions for nonlinear ordinary differential equations. The first section of the chapter investigates a nonlinear periodic problem involving the scalar p-Laplacian for 1 < p < + in the principal part and a smooth potential. The results cover cases of resonance at any eigenvalue of the principal part. They are obtained through variational methods and Morse theory. The second section presents results on the existence of multiple solutions for a second-order periodic system in the form of a differential inclusion. The multivalued term is expressed as a generalized gradient of a locally Lipschitz function. The approach is based on nonsmooth critical point theory. Comments and relevant references are given in a remarks section.

Keywords

Manifold 

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Copyright information

© Springer Science+Business Media, LLC 2014

Authors and Affiliations

  • Dumitru Motreanu
    • 1
  • Viorica Venera Motreanu
    • 2
  • Nikolaos Papageorgiou
    • 3
  1. 1.Department of MathematicsUniversity of PerpignanPerpignanFrance
  2. 2.Department of MathematicsBen-Gurion University of the NegevBeer-ShevaIsrael
  3. 3.Department of MathematicsNational Technical UniversityAthensGreece

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