Abstract
In this paper, we shall be concerned with the existence of renormalized solution of the following problem,
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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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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DOI: https://doi.org/10.1007/s11587-017-0322-3
Keywords
- Nonlinear elliptic problems
- Non-polynomial growth
- Orlicz-Sobolev spaces
- Renormalized solutions
- Lower order terms