Study of Some Non-linear Elliptic Problems with No Continuous Lower Order Terms in Orlicz Spaces
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- 作者：H. Moussa ; M. Rhoudaf
- 关键词：Elliptic problems ; Orlicz spaces ; Renormalized solutions ; Lower order terms
- 刊名：Mediterranean Journal of Mathematics
- 出版年：2016
- 出版时间：December 2016
- 年：2016
- 卷：13
- 期：6
- 页码：4867-4899
- 全文大小：747 KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics - 出版者：Birkh盲user Basel
- ISSN：1660-5454
- 卷排序：13
文摘
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.