Existence Results for Nonlinear Elliptic Equations with Leray–Lions Operators in Sobolev Spaces with Variable Exponents

2021 ◽  
Vol 110 (5-6) ◽  
pp. 830-841
Author(s):  
M. Mosa Al-Shomrani ◽  
M. Ben Mohamed Salah ◽  
A. Ghanmi ◽  
K. Kefi
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Existence Results ◽  
Variable Exponents ◽  
Nonlinear Elliptic

scholarly journals Nonlinear elliptic equations with variable exponents involving singular nonlinearity

2021 ◽  
Vol 8 (4) ◽  
pp. 705-715
Author(s):  
H. Khelifi ◽  
◽  
Y. El Hadfi ◽  
◽  
Keyword(s):  
Sobolev Spaces ◽  
Lower Order ◽  
Elliptic Equations ◽  
Order Term ◽  
Nonlinear Elliptic Equations ◽  
Variable Exponents ◽  
Singular Nonlinearity ◽  
Nonlinear Elliptic ◽  
Regularizing Effects ◽  
Lower Order Terms

In this paper, we prove the existence and regularity of weak positive solutions for a class of nonlinear elliptic equations with a singular nonlinearity, lower order terms and L1 datum in the setting of Sobolev spaces with variable exponents. We will prove that the lower order term has some regularizing effects on the solutions. This work generalizes some results given in [1–3].

scholarly journals Entropy and renormalized solutions for some nonlinear anisotropic elliptic equations with variable exponents and L 1-data

2021 ◽  
Vol 7 (2) ◽  
pp. 277-298
Author(s):  
Mostafa El Moumni ◽  
Deval Sidi Mohamed
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Variable Exponents ◽  
Renormalized Solutions ◽  
Nonlinear Elliptic ◽  
Anisotropic Elliptic Equations

Abstract We prove in this paper some existence and unicity results of entropy and renormalized solutions for some nonlinear elliptic equations with general anisotropic diffusivities and variable exponents. The data are assumed to be merely integrable.

Existence results for the Dirichlet problem of some degenerate nonlinear elliptic equations

2014 ◽  
Vol 20 (2) ◽  
Author(s):  
Albo Carlos Cavalheiro
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Nonlinear Elliptic Equations ◽  
Existence Results ◽  
Uniqueness Of Solutions ◽  
Nonlinear Elliptic

AbstractIn this paper we are interested in the existence and uniqueness of solutions for the Dirichlet problem associated to the degenerate nonlinear elliptic equations

scholarly journals Existence Results For A Class Of Nonlinear Degenerate Elliptic Equations

2019 ◽  
Vol 5 (2) ◽  
pp. 164-178
Author(s):  
Albo Carlos Cavalheiro
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Weighted Sobolev Spaces ◽  
Nonlinear Elliptic Equations ◽  
Existence Results ◽  
Degenerate Elliptic Equations ◽  
Nonlinear Elliptic ◽  
Degenerate Elliptic ◽  
Nonlinear Degenerate

AbstractIn this paper we are interested in the existence of solutions for Dirichlet problem associated with the degenerate nonlinear elliptic equations\left\{ {\matrix{ { - {\rm{div}}\left[ {\mathcal{A}\left( {x,\nabla u} \right){\omega _1} + \mathcal{B}\left( {x,u,\nabla u} \right){\omega _2}} \right] = {f_0}\left( x \right) - \sum\limits_{j = 1}^n {{D_j}{f_j}\left( x \right)\,\,{\rm{in}}} \,\,\,\,\,\Omega ,} \hfill \cr {u\left( x \right) = 0\,\,\,\,{\rm{on}}\,\,\,\,\partial \Omega {\rm{,}}} \hfill \cr } } \right.in the setting of the weighted Sobolev spaces.

Sign in / Sign up

Export Citation Format

Share Document