Topological Methods in Nonlinear Analysis

Nonlinear periodic system with unilateral constraints

Sergiu Aizicovici, Nikolaos S. Papageorgiou, and Vasile Staicu

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Abstract

We consider a general periodic system driven by a nonlinear, nonhomogeneous differential operator, with a maximal monotone term which is not defined everywhere. Using a topological approach based on Leray-Schauder alternative principle, we show the existence of a periodic solution.

Article information

Source
Topol. Methods Nonlinear Anal., Advance publication (2019), 15 pp.

Dates
First available in Project Euclid: 11 November 2019

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1573441225

Digital Object Identifier
doi:10.12775/TMNA.2019.062

Citation

Aizicovici, Sergiu; Papageorgiou, Nikolaos S.; Staicu, Vasile. Nonlinear periodic system with unilateral constraints. Topol. Methods Nonlinear Anal., advance publication, 11 November 2019. doi:10.12775/TMNA.2019.062. https://projecteuclid.org/euclid.tmna/1573441225


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References

  • S. Aizicovici, N.S. Papageorgiou and V. Staicu, Nodal and multiple solutions for nonlinear periodic problems with competing nonlinearities, Commun. Contemp. Math. 15 (2013), no. 3, 1350001–1350030.
  • S. Aizicovici, N.S. Papageorgiou and V. Staicu, Nonlinear, nonconvex second order multivalued systems with maximal monotone terms, Pure Appl. Funct. Anal. 2 (2017), 553–574.
  • L. Gasinski and N.S. Papageorgiou, Nonlinear Analysis, Chapman & Hall/CRC Press, Boca Raton, 2006.
  • P. Hartman, On boundary value problems for systems of ordinary nonlinear second order differential equations, Trans. Amer. Math. Soc. 96 (1960), 493–509.
  • H.W. Knobloch, On the existence of periodic solutions for second order vector differential equations, J. Differential Equations 9 (1971), 67–85.
  • H.W. Knobloch and K. Schmitt, Nonlinear boundary value problems for systems of differential equations, Proc. Roy. Soc. Edinburgh Sect. A 78 (1977), 139–159.
  • R. Manasevich and J. Mawhin, Periodic solutions for nonlinear systems with $p$-Laplacian-like operators, J. Differential Equations 145 (1998), 367–393.
  • M. Marcus and V. Mizel, Absolute continuity on tracks and mappings of Sobolev spaces, Arch. Ration. Mech. Anal. 45 (1972), 294–320.
  • J. Mawhin, Some boundary value problems for Harman-type perturbations of the ordinary vector $p$-Laplacian, Nonlinear Anal. 40 (2000), 497–503.
  • I. Vrabie, Compactness Methods for Nonlinear Evolutions, Longman Scientific and Technical, Harlow, Essex, 1987.