On various questions of the existence of an approximate solution for quasilinear elliptic equations and systems in S. L. Sobolev spaces

1968 ◽  
Vol 9 (5) ◽  
pp. 875-882 ◽  
Author(s):  
A. I. Koshelev
Keyword(s):  
Approximate Solution ◽  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Quasilinear Elliptic

Existence of Solutions in Weighted Sobolev Spaces for Some Degenerate Quasilinear Elliptic Equations

2008 ◽  
Vol 15 (4) ◽  
pp. 627-634
Author(s):  
Albo Carlos Cavalheiro
Keyword(s):  
Dirichlet Problem ◽  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Existence Result ◽  
Existence Of Solutions ◽  
Weighted Sobolev Spaces ◽  
Quasilinear Elliptic Equations ◽  
Open Set ◽  
Quasilinear Elliptic

Abstract We prove an existence result for the Dirichlet problem associated to some degenerate quasilinear elliptic equations in a bounded open set Ω in in the setting of weighted Sobolev spaces .

scholarly journals The Sub-Supersolution Method and Extremal Solutions of Quasilinear Elliptic Equations in Orlicz-Sobolev Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Ge Dong ◽  
Xiaochun Fang
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Nonlinear Term ◽  
Extremal Solutions ◽  
Quasilinear Elliptic Equations ◽  
Quasilinear Elliptic Problem ◽  
Analysis Theory ◽  
Carathéodory Function ◽  
Quasilinear Elliptic ◽  
Differential Part

We prove the existence of extremal solutions of the following quasilinear elliptic problem -∑i=1N∂/∂xiai(x,u(x),Du(x))+g(x,u(x),Du(x))=0 under Dirichlet boundary condition in Orlicz-Sobolev spaces W01LM(Ω) and give the enclosure of solutions. The differential part is driven by a Leray-Lions operator in Orlicz-Sobolev spaces, while the nonlinear term g:Ω×R×RN→R is a Carathéodory function satisfying a growth condition. Our approach relies on the method of linear functional analysis theory and the sub-supersolution method.

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