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Asymptotic Behaviour of Some Equations in Orlicz Spaces  
 
  Authors: A. Elmahi, D. Meskine,  
  Keywords: Strongly nonlinear elliptic equations, Natural growth, Truncations, Variational inequalities, Bilateral problems.  
  Date Received: 26/03/03  
  Date Published: 05/08/03  
  Subject Codes:

35J25,35J60.

  
  Editors: Alberto Fiorenza,  
 
  Abstract:

In this paper, we prove an existence and uniqueness result for solutions of some bilateral problems of the form

$displaystyle left{ begin{array}{l} langle Au, v-u rangle geq langle f, v u rangle , forall vin K [10pt] uin K end{array} right.$   
where $ A$ is a standard Leray-Lions operator defined on $ W_{0}^{1}L_{M}(Omega)$, with $ M$ an N-function which satisfies the $ Delta_2$-condition, and where $ K$ is a convex subset of $ W_{0}^{1}L_{M}(Omega)$ with obstacles depending on some Carathéodory function $ g(x,u)$. We consider first, the case $ fin W^{-1}E_{overline M}(Omega)$ and secondly where $ fin L^{1}(Omega)$. Our method deals with the study of the limit of the sequence of solutions$ u_n$ of some approximate problem with nonlinearity term of the form $ vert g(x,u_n)vert^{n-1}g(x,u_n)times M(vertnabla u_nvert)$.
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