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Study of Some Non-linear Elliptic Problems with No Continuous Lower Order Terms in Orlicz Spaces

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Abstract

In this study, we shall be concerned with the existence result of the non-linear elliptic equations of the form, \({Au-div(\Phi(x,u)) = f,}\) where the term \({Au=-div(a(x,u,\nabla u))}\) is a Leray–Lions operator defined on \({W_0^{1}L_M(\Omega)}\) into its dual \({W^{-1}L_{\overline{M}}(\Omega)}\), where \({M}\) is an \({N}\)-function without assuming a \({\Delta_2}\)-condition on \({M}\), the second term \({f}\) belongs to \({L^1(\Omega)}\), and the function \({\Phi}\) is not a continuous function with respect to \({x}\) which cannot be managed by the divergence Theorem.

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  1. Department of Mathematics, Moulay Ismail University, Faculty of Sciences, 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. Study of Some Non-linear Elliptic Problems with No Continuous Lower Order Terms in Orlicz Spaces. Mediterr. J. Math. 13, 4867–4899 (2016). https://doi.org/10.1007/s00009-016-0780-y

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