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Existence of renormalized solution of nonlinear elliptic problems with lower order term in Orlicz spaces

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Abstract

In this paper, we shall be concerned with the existence of renormalized solution of the following problem,

$$\begin{aligned} \left\{ \begin{array}{l} -\text {div}\Big (a(x,u,\nabla u)\Big )-\text {div}(\Phi (x,u))= f \ \ \mathrm{in}\ \Omega ,\\ u=0 \text { on } \partial \Omega , \end{array} \right. \end{aligned}$$

with the second term f belongs to \(L^1(\Omega )\). The growth and the coercivity conditions on the monotone vector field a are prescribed by a N-function M. We assume any restriction on M, therefore we work with Orlicz-Sobolev spaces which are not necessarily reflexive. The lower order term \(\Phi \) is a Carathéodory function which is not coercive.

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  1. Département Mathématiques, Faculté des Sciences Meknés, Université Moulay Ismail, Meknes, Morocco

    H. Moussa & M. Rhoudaf

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  1. H. Moussa
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  2. M. Rhoudaf
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Moussa, H., Rhoudaf, M. Existence of renormalized solution of nonlinear elliptic problems with lower order term in Orlicz spaces. Ricerche mat 66, 591–617 (2017). https://doi.org/10.1007/s11587-017-0322-3

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