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Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 29))

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

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6820-5

  • Online ISBN: 978-1-4615-4064-9

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