Existence of Solutions for Unbounded Elliptic Equations with Critical Natural Growth

We investigate existence and regularity of solutions to unbounded elliptic problem whose simplest model is {-div[(1+uq)∇u]+u=γ∇u2/1+u1-q+f  in  Ω,  u=0  on  ∂Ω,}, where 0<q<1, γ>0 and f belongs to some appropriate Lebesgue space. We give assumptions on f with respect to q and γ to show the...

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Main Authors: Aziz Bouhlal, Abderrahmane El Hachimi, Jaouad Igbida, El Mostafa Sadek, Hamad Talibi Alaoui
Format: Article
Language:English
Published: Wiley 2018-01-01
Series:International Journal of Differential Equations
Online Access:http://dx.doi.org/10.1155/2018/7434250
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author Aziz Bouhlal
Abderrahmane El Hachimi
Jaouad Igbida
El Mostafa Sadek
Hamad Talibi Alaoui
author_facet Aziz Bouhlal
Abderrahmane El Hachimi
Jaouad Igbida
El Mostafa Sadek
Hamad Talibi Alaoui
author_sort Aziz Bouhlal
collection DOAJ
description We investigate existence and regularity of solutions to unbounded elliptic problem whose simplest model is {-div[(1+uq)∇u]+u=γ∇u2/1+u1-q+f  in  Ω,  u=0  on  ∂Ω,}, where 0<q<1, γ>0 and f belongs to some appropriate Lebesgue space. We give assumptions on f with respect to q and γ to show the existence and regularity results for the solutions of previous equation.
format Article
id doaj-art-820d1d29ab2f42fcb629af1aa5fdeb9f
institution OA Journals
issn 1687-9643
1687-9651
language English
publishDate 2018-01-01
publisher Wiley
record_format Article
series International Journal of Differential Equations
spelling doaj-art-820d1d29ab2f42fcb629af1aa5fdeb9f2025-08-20T02:09:05ZengWileyInternational Journal of Differential Equations1687-96431687-96512018-01-01201810.1155/2018/74342507434250Existence of Solutions for Unbounded Elliptic Equations with Critical Natural GrowthAziz Bouhlal0Abderrahmane El Hachimi1Jaouad Igbida2El Mostafa Sadek3Hamad Talibi Alaoui4Labo Math Appli, Faculty of Sciences, B. P. 20, El Jadida, MoroccoLaboratory of Mathematical Analysis and Applications, Mohammed V University, Faculty of Sciences, Rabat, MoroccoLabo DGTIC, department of Mathematics, CRMEF El Jadida, MoroccoLaboratory LabSIPE, ENSA, d'EL Jadida, University Chouaib Doukkali, MoroccoLabo Math Appli, Faculty of Sciences, B. P. 20, El Jadida, MoroccoWe investigate existence and regularity of solutions to unbounded elliptic problem whose simplest model is {-div[(1+uq)∇u]+u=γ∇u2/1+u1-q+f  in  Ω,  u=0  on  ∂Ω,}, where 0<q<1, γ>0 and f belongs to some appropriate Lebesgue space. We give assumptions on f with respect to q and γ to show the existence and regularity results for the solutions of previous equation.http://dx.doi.org/10.1155/2018/7434250
spellingShingle Aziz Bouhlal
Abderrahmane El Hachimi
Jaouad Igbida
El Mostafa Sadek
Hamad Talibi Alaoui
Existence of Solutions for Unbounded Elliptic Equations with Critical Natural Growth
International Journal of Differential Equations
title Existence of Solutions for Unbounded Elliptic Equations with Critical Natural Growth
title_full Existence of Solutions for Unbounded Elliptic Equations with Critical Natural Growth
title_fullStr Existence of Solutions for Unbounded Elliptic Equations with Critical Natural Growth
title_full_unstemmed Existence of Solutions for Unbounded Elliptic Equations with Critical Natural Growth
title_short Existence of Solutions for Unbounded Elliptic Equations with Critical Natural Growth
title_sort existence of solutions for unbounded elliptic equations with critical natural growth
url http://dx.doi.org/10.1155/2018/7434250
work_keys_str_mv AT azizbouhlal existenceofsolutionsforunboundedellipticequationswithcriticalnaturalgrowth
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AT jaouadigbida existenceofsolutionsforunboundedellipticequationswithcriticalnaturalgrowth
AT elmostafasadek existenceofsolutionsforunboundedellipticequationswithcriticalnaturalgrowth
AT hamadtalibialaoui existenceofsolutionsforunboundedellipticequationswithcriticalnaturalgrowth