# American Institute of Mathematical Sciences

August  2012, 5(4): 809-818. doi: 10.3934/dcdss.2012.5.809

## On the existence of nontrivial solutions of inequalities in Orlicz-Sobolev spaces

 1 Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409, United States

Received  February 2011 Revised  April 2011 Published  November 2011

This paper is about an alternate variational inequality formulation for the boundary value problem $$\begin{array}{l} -{\rm div} (a(|\nabla u|) \nabla u) + \partial_u G(x,u) \ni 0 \;\mbox{ in } \;\Omega , \\ u=0 \;\mbox{ on } \;\partial\Omega , \end{array}$$ where the principal part may have non-polynomial or very slow growth. As a consequence of this formulation, we can apply abstract nonsmooth linking theorems to study the existence and multiplicity of nontrivial solutions to the above problem.
Citation: Vy Khoi Le. On the existence of nontrivial solutions of inequalities in Orlicz-Sobolev spaces. Discrete & Continuous Dynamical Systems - S, 2012, 5 (4) : 809-818. doi: 10.3934/dcdss.2012.5.809
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