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    STUDIA MATHEMATICA - Issue no. 4 / 2010  
         
  Article:   COMBINED VARIATIONAL AND SUB-SUPERSOLUTION APPROACH FOR MULTI-VALUED ELLIPTIC VARIATIONAL INEQUALITIES.

Authors:  . 		 
       
         
  Abstract:  This paper provides a variational approach for a class of multi-valued elliptic variational inequalities governed by the p-Laplacian and Clarke’s generalized gradient of some locally Lipschitz function including a number of (multi-valued) elliptic boundary value problems as special cases. Since only local growth conditions are imposed on the multi-valued term, the problem under consideration is neither coercive nor of variational structure beforehand meaning that it cannot be related to the derivative of some associated (nonsmooth) potential. By combining a recently developed sub-supersolution method for multi-valued elliptic variational inequalities and a suitable modification of the given locally Lipschitz function the main goal of this paper is to construct a (nonsmooth) functional whose critical points turn out to be solutions of the problem under consideration lying in an ordered interval of sub-supersolution.

Key words and phrases. Multi-valued variational inequality, p-Laplacian, Clarke’s generalized gradient, sub-supersolution, critical point, locally Lipschitz functional, comparison principle. 

 
         
     
         
         
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