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Periodic and Dynamic Problems

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Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 29))

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Abstract

The present chapter is devoted to the study of some evolutive or periodic hemivariational inequalities. Specifically, it contains the following three types of problems: hyperbolic hemivariational inequalities modelling nonlinear wave equations with nonlinearities, homoclinic solutions for second order Hamiltonian systems with discontinuous nonlinearities, and multiplicity results for hemivariational inequalities involving periodic energy functionals. The existence of solutions of nonsmooth hyperbolic problems expressed in the form of a hemivariational inequality are studied separately in the nonresonant and the resonant cases. The second section of the chapter contains some existence and multiplicity results for periodic solutions of second order nonautonomous and nonsmooth Hamiltonian systems involving nonconvex superpotentials. These results are proved by showing the existence of homoclinic solutions which are constructed as critical points of the corresponding nonconvex and nonsmooth energy functional.

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Authors and Affiliations

  1. Department of Mathematics, University of Iasi, Romania

    D. Motreanu

  2. Department of Civil Engineering, Aristotle University, Thessaloniki, Greece

    P. D. Panagiotopoulos

  3. Faculty of Mathematics and Physics, RWTH Aachen, Germany

    P. D. Panagiotopoulos

Authors
  1. D. Motreanu
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  2. P. D. Panagiotopoulos
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© 1999 Springer Science+Business Media Dordrecht

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Motreanu, D., Panagiotopoulos, P.D. (1999). Periodic and Dynamic Problems. In: Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities. Nonconvex Optimization and Its Applications, vol 29. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4064-9_9

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  • DOI: https://doi.org/10.1007/978-1-4615-4064-9_9

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6820-5

  • Online ISBN: 978-1-4615-4064-9

  • eBook Packages: Springer Book Archive

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