Strongly nonlinear elliptic equations having natural growth terms and L1 data

1992 ◽  
Vol 19 (6) ◽  
pp. 573-579 ◽  
Author(s):  
L. Boccardo ◽  
T. Gallouet
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Natural Growth ◽  
Strongly Nonlinear ◽  
Nonlinear Elliptic ◽  
L1 Data ◽  
Natural Growth Terms

scholarly journals Existence of solutions for elliptic equations having natural growth terms in Orlicz spaces

2004 ◽  
Vol 2004 (12) ◽  
pp. 1031-1045 ◽  
Author(s):  
A. Elmahi ◽  
D. Meskine
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equation ◽  
Existence Result ◽  
Existence Of Solutions ◽  
Orlicz Spaces ◽  
Natural Growth ◽  
Strongly Nonlinear ◽  
Nonlinear Elliptic ◽  
Natural Growth Terms

Existence result for strongly nonlinear elliptic equation with a natural growth condition on the nonlinearity is proved.

scholarly journals Existence of entropy solutions for nonlinear elliptic equations in Musielak framework with L1 data

2018 ◽  
Vol 36 (1) ◽  
pp. 125 ◽  
Author(s):  
Elemine Vall Mohamed Saad Bouh ◽  
A. Ahmed ◽  
A. Touzani ◽  
A. Benkirane
Keyword(s):  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Nonlinear Elliptic Equations ◽  
Entropy Solutions ◽  
Strongly Nonlinear ◽  
Nonlinear Elliptic ◽  
Right Hand ◽  
L1 Data ◽  
The Right

We prove existence of solutions for strongly nonlinear elliptic equations of the form $$ \left\{\begin{array}{c} A(u)+g(x,u,\nabla u)=f+\mbox {div}(\phi(u))\quad \textrm{in }\Omega, \\ u\equiv0\quad \partial \Omega. \end{array} \right.$$ Where $A(u)=-\mbox {div}(a(x,u,\nabla u))$ be a Leray-Lions operator defined in $D(A)\subset W^{1}_{0}L_\varphi(\Omega) \rightarrow W^{-1}_{0}L_\psi(\Omega)$, the right hand side belongs in $ L^{1}(\Omega)$, and $\phi\in C^{0}(\mathbb{R},\mathbb{R}^N)$, without assuming the $\Delta_{2}$-condition on the Musielak function.

scholarly journals Non-linear elliptic unilateral problems in Musielak-Orlicz spaces with L1 data

2018 ◽  
Vol 36 (1) ◽  
pp. 51
Author(s):  
Mustafa Ait Khellou ◽  
Abdelmoujib Benkirane
Keyword(s):  
Sobolev Space ◽  
Existence Result ◽  
Orlicz Spaces ◽  
Conjugate Function ◽  
Natural Growth ◽  
Nonlinear Elliptic ◽  
L1 Data ◽  
Non Linear ◽  
Unilateral Problems ◽  
Natural Growth Terms

We prove an existence result of solutions for nonlinear elliptic unilateral problems having natural growth terms and L1 data in Musielak-Orlicz-Sobolev space W1Lφ, under the assumption that the conjugate function of φ satisfies the ∆2-condition.

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