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    STUDIA MATHEMATICA - Issue no. 3 / 2013  
         
  Article:   AN EXISTENCE RESULT FOR NONLINEAR HEMIVARIATIONAL-LIKE INEQUALITY SYSTEMS.

Authors:  ANDREA-ÉVA MOLNÁR.
 
       
         
  Abstract:   In this paper, we introduce and study a system of nonlinear hemivariational-like inequality system in reflexive Banach spaces. The novelty of our approach is that we prove the existence of at least one solution for our system without imposing any monotonicity assumptions or using nonsmooth critical point theory. The main tool is a fixed theorem due to T.C. Lin [Bull. Aust. Math. Soc. 34 (1986), 107-117.] Two applications are also given: the first one prove the existence of Nash generalized derivative points, while the second one the existence of at least one solution of a Schrödinger-type problem.

Mathematics Subject Classification (2010): 47J20, 54C60, 47H10.
Keywords: Fixed point theory, hemivariational inequality system, locally Lipschitzfunctional, set-valued operator.
 
         
     
         
         
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