scholarly journals Existence of Solution for Nonlinear Elliptic Equations with Unbounded Coefficients and Data

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
Hicham Redwane
Keyword(s):  
Elliptic Equations ◽  
Existence Result ◽  
Nonlinear Elliptic Equations ◽  
Existence Of Solution ◽  
Unbounded Coefficients ◽  
Renormalized Solution ◽  
Nonlinear Elliptic

An existence result of a renormalized solution for a class of nonlinear elliptic equations is established. The diffusion functions may not be in for a finite value of the unknown and the data belong to .

scholarly journals Existence results for a perturbed Dirichlet problem without sign condition in Orlicz spaces

2020 ◽  
Vol 72 (4) ◽  
pp. 509-526
Author(s):  
H. Moussa ◽  
M. Rhoudaf ◽  
H. Sabiki
Keyword(s):  
Elliptic Equations ◽  
Existence Result ◽  
Orlicz Spaces ◽  
Nonlinear Elliptic Equations ◽  
Existence Results ◽  
Nonlinear Elliptic ◽  
Sign Condition ◽  
Carathéodory Function ◽  
Monotone Vector Field ◽  
The Right

UDC 517.5 We deal with the existence result for nonlinear elliptic equations related to the form < b r > A u + g ( x , u , ∇ u ) = f , < b r > where the term - ⅆ i v ( a ( x , u , ∇ u ) ) is a Leray–Lions operator from a subset of W 0 1 L M ( Ω ) into its dual.  The growth and coercivity conditions on the monotone vector field a are prescribed by an N -function M which does not have to satisfy a Δ 2 -condition. Therefore we use Orlicz–Sobolev spaces which are not necessarily reflexive and assume that the nonlinearity g ( x , u , ∇ u ) is a Carathéodory function satisfying only a growth condition with no sign condition. The right-hand side~ f belongs to W -1 E M ¯ ( Ω ) .

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

2015 ◽  
Vol 22 (3) ◽  
Author(s):  
Azeddine Aissaoui Fqayeh ◽  
Abdelmoujib Benkirane ◽  
Mostafa El Moumni ◽  
Ahmed Youssfi
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equations ◽  
Orlicz Spaces ◽  
Nonlinear Elliptic Equations ◽  
Renormalized Solutions ◽  
Renormalized Solution ◽  
Strongly Nonlinear ◽  
Nonlinear Elliptic

AbstractWe prove the existence of a renormalized solution for the Dirichlet problem associated to the nonlinear elliptic equations div

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