Abstract
A general min–max principle established by Ghoussoub is extended to the case of functionals f which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function, when f satisfies a compactness condition weaker than the Palais–Smale one, i.e., the so-called Cerami condition. Moreover, an application to a class of elliptic variational–hemivariational inequalities in the resonant case is presented.
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Livrea, R., Bisci, G.M. Some remarks on nonsmooth critical point theory. J Glob Optim 37, 245–261 (2007). https://doi.org/10.1007/s10898-006-9047-7
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DOI: https://doi.org/10.1007/s10898-006-9047-7
Keywords
- Critical points for nonsmooth functions
- Nonsmooth Cerami condition
- Elliptic variational–hemivariational inequalities
- Problem at risonance