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

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  • 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.
    Mathematics Subject Classification: Primary: 35B45, 35J65, 35J60.


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