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Applied Mathematics & Optimization

, Volume 78, Issue 1, pp 1–23 | Cite as

Nonlinear Elliptic Inclusions with Unilateral Constraint and Dependence on the Gradient

  • Nikolaos S. Papageorgiou
  • Vicenţiu D. Rădulescu
  • Dušan D. Repovš
Article

Abstract

We consider a nonlinear Neumann elliptic inclusion with a source (reaction term) consisting of a convex subdifferential plus a multivalued term depending on the gradient. The convex subdifferential incorporates in our framework problems with unilateral constraints (variational inequalities). Using topological methods and the Moreau-Yosida approximations of the subdifferential term, we establish the existence of a smooth solution.

Keywords

Convex subdifferential Moreau-Yosida approximation Elliptic differential inclusion Morse iteration technique Pseudomonotone map Variational inequality 

Mathematics Subject Classification

35J60 35K85 

Notes

Acknowledgements

V. Rădulescu was supported by a grant of the Romanian National Authority for Scientific Research and Innovation, CNCS-UEFISCDI, Project Number PN-II-PT-PCCA-2013-4-0614. D. Repovš was supported by the Slovenian Research Agency Grants P1-0292-0101, J1-6721-0101, J1-7025-0101 and J1-5435-0101.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Nikolaos S. Papageorgiou
    • 1
  • Vicenţiu D. Rădulescu
    • 2
    • 3
  • Dušan D. Repovš
    • 4
  1. 1.Department of MathematicsNational Technical UniversityAthensGreece
  2. 2.Department of Mathematics, Faculty of SciencesKing Abdulaziz UniversityJeddahSaudi Arabia
  3. 3.Department of MathematicsUniversity of CraiovaCraiovaRomania
  4. 4.Faculty of Education and Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia

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