Abstract
The aim of this chapter is to present general results, many of them belonging to the authors, that can be applied to locally Lipschitz functionals, possibly invariant under a compact Lie group of linear isometries. The nonsmooth critical point theory in the locally Lipschitz case originates in the work of Chang [4]. Here the results of Chang [4] are deduced from a general principle that also incorporates the results of Du [7]. Our minimax principles are based on a deformation theorem that unifies different classical deformation results. Two main ideas are the bases of the mathematical approach in this chapter: the linking properties and the equivariance theory. A certain structure of the locally Lipschitz functionals that is particularly appropriate in the setting of our minimax methods is also pointed out. The applications of the abstract critical point results refer to nonsmooth elliptic boundary value problems.
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Motreanu, D., Panagiotopoulos, P.D. (1999). Nonsmooth Critical Point Theory. 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_2
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