Abstract
The present Chapter deals with critical point theory for three different nonsmooth situations. First, we set forth the critical point theory for locally Lipschitz functionals, following the approach of Chang [4] and Clarke [5]. Then a critical point theory is described for nonsmooth functionals expressed as a sum of a locally Lipschitz function and a convex, proper and lower semicontinuous function, using the development in Motreanu and Panagiotopoulos [26]. Finally, the critical point theory for continuous functionals defined on a complete metric space as introduced by Degiovanni and Marzocchi [7] is presented.
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Motreanu, D., Rădulescu, V. (2003). Critical Points for Nonsmooth Functionals. In: Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems. Nonconvex Optimization and Its Applications, vol 67. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6921-0_2
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DOI: https://doi.org/10.1007/978-1-4757-6921-0_2
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