Minimax Theorems for Locally Lipschitz Functionals and Applications
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.
KeywordsGeneralize Gradient Directional Derivative Convergent Subsequence Critical Point Theory Minimax Theorem
Unable to display preview. Download preview PDF.
- [Au]Aubin, Jean-Pierre. L ’analyse Non Linéaire et ses Motivations Economique. Paris: Masson, 1984.Google Scholar
- [GT1]Grossinho MR, Tersian S. Critical point theory for locally Lipschitz functionals and applications to fourth order problems. Proceedings of XXVIII-th Spring Conference of U.B.M., Sofia, 1999:99–106.Google Scholar
- [Wil1]Willem M. Lecture notes on critical point theory, Fundação Universidade de Brasília, 199, 1983.Google Scholar