Abstract
The present chapter deals with the mathematical study of the resonant case of eigenvalue problems for hemivariational inequalities. One obtains new Landesman-Lazer type results allowing unbounded nonlinearities and resonance at multiple eigenvalues. A buckling problem in Mechanics illustrates the practical motivation and the interest in these topics. We use two different methods: a nonsmooth version of the Saddle-Point Theorem due to K. C. Chang and the Leray-Schauder topological degree. The results of this chapter improve and extend all the known results related to the nonsmooth resonant eigenvalue problems.
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Motreanu, D., Panagiotopoulos, P.D. (1999). Resonant Eigenvalue Problems for Hemivariational Inequalities. 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_7
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DOI: https://doi.org/10.1007/978-1-4615-4064-9_7
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