Minimax Theorems for Locally Lipschitz Functionals and Applications

  • Maria do Rosário Grossinho
  • Stepan Agop Tersian
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 52)


The purpose of this chapter is to present several variants of minimization and mountain-pass theorems for nondifferentiable functionals. We assume that the given functionals are locally Lipschitz so that their generalized gradients can be defined (cf. Clarke [Cl] ). A general critical point theory for locally Lipschitz functionals was developed by K. C. Chang [Ch1], extending the concept of a critical point, the Palais—Smale condition and the deformation lemma. Critical point results have also been obtained in other nondifferentiable settings. We refer to Degiovanni & Marzocchi [DM], Corvellec, Degiovanni & Marzocchi [CDM] for the case of continuous functionals and to Ribarska, Tsachev & Krastanov [RTK1], Ioffe & Schwartzman [IS] for the case of discontinuous functionals.


Generalize Gradient Directional Derivative Convergent Subsequence Critical Point Theory Minimax Theorem 


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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Maria do Rosário Grossinho
    • 1
    • 2
  • Stepan Agop Tersian
    • 3
  1. 1.ISEGUniversidade Técnica de LisboaPortugal
  2. 2.CMAFUniversidade de LisboaPortugal
  3. 3.University of RousseBulgaria

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