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Existence of renormalized solutions for some nonlinear elliptic equations in Orlicz spaces

  • M. BourahmaEmail author
  • A. Benkirane
  • J. Bennouna
Article
  • 12 Downloads

Abstract

In this work, we prove an existence theorem of renormalized solutions for nonlinear elliptic problem of the type
$$\begin{aligned} -{\text {div}}\>a(x,u,\nabla u)-\mathop {{\mathrm{div}}}\Phi (x,u)= f \quad \text {in }{\Omega }, \end{aligned}$$
where the lower order term \(\Phi \) verifies the natural growth condition
$$\begin{aligned} |\Phi (x,s)|\le \gamma (x)+\overline{M}^{-1}(M(|s|)), \text { with } \gamma \in E_{\overline{M}}(\Omega ). \end{aligned}$$
No \(\Delta _{2}\)-condition is needed neither on the N-function M nor on its complementary \(\overline{M}\).

Keywords

Elliptic problem Orlicz spaces Renormalized solutions 

Mathematics Subject Classification

35J60 

Notes

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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Laboratory LAMA, Department of Mathematics, Faculty of Sciences Dhar el MahrazSidi Mohamed Ben Abdellah UniversityFez-Atlas, FezMorocco

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