Journal of Global Optimization

, Volume 34, Issue 2, pp 219–244

“Two Nontrivial Critical Points for Nonsmooth Functionals via Local Linking and Applications”

  • Dimitrios Kandilakis
  • Nikolaos C. Kourogenis
  • Nikolaos S. Papageorgiou
Article

DOI: 10.1007/s10898-005-3884-7

Cite this article as:
Kandilakis, D., Kourogenis, N.C. & Papageorgiou, N.S. J Glob Optim (2006) 34: 219. doi:10.1007/s10898-005-3884-7

Abstract

In this paper, we extend to nonsmooth locally Lipschitz functionals the multiplicity result of Brezis–Nirenberg (Communication Pure Applied Mathematics and 44 (1991)) based on a local linking condition. Our approach is based on the nonsmooth critical point theory for locally Lipschitz functions which uses the Clarke subdifferential. We present two applications. This first concerns periodic systems driven by the ordinary vector p-Laplacian. The second concerns elliptic equations at resonance driven by the partial p-Laplacian with Dirichlet boundary condition. In both cases the potential function is nonsmooth, locally Lipschitz.

Keywords

Cerami condition Critical point Generalized subdifferential Local linking Locally Lipschitz function Nonsmooth critical point theory Periodic system p-Laplacian Principal eigenvalue Problem at resonance 

AMS Subject Classifications (2000)

35J20 35J85 34C25 

Copyright information

© Springer 2006

Authors and Affiliations

  • Dimitrios Kandilakis
    • 1
  • Nikolaos C. Kourogenis
    • 2
  • Nikolaos S. Papageorgiou
    • 3
  1. 1.Department of MathematicsTechnical University of CreteCreteGreece
  2. 2.Department of Applied MathematicsUniversity of CreteCreteGreece
  3. 3.Department of MathematicsNational Technical UniversityAthensGreece

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