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Location of Solutions for General Nonsmooth Problems

  • D. Motreanu
  • V. Rădulescu
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 67)

Abstract

The aim of the present Chapter is to study from a qualitative point of view a general eigenvalue problem associated to a variational-hemivariational inequality with a constraint for the eigenvalue. The basic feature of our approach is that we are mainly concerned with the location of eigensolution (u, λ), where u and λ stand for the eigenfunction and the eigenvalue, respectively. This is done in Section 2, where the location of eigensolutions is achieved by means of the graph of the derivative of a C 1 function. Section 1 presents a general existence result for variationalhemivariational inequalities with assumptions of Ambrosetti and Rabinowitz type. Section 2 deals with the exposition of our abstract location results. In Section 3 we discuss the location of solutions to variationalhemivariational inequalities by applying the abstract results. The case of nonlinear Dirichlet boundary value problems is contained.

Keywords

Eigenvalue Problem Variational Method Generalize Gradient Real Hilbert Space Critical Point Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • D. Motreanu
    • 1
  • V. Rădulescu
    • 2
  1. 1.Department of MathematicsUniversity of PerpignanPerpignanFrance
  2. 2.Department of MathematicsUniversity of CraiovaCraiovaRomania

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