Sub-supersolution method for nonlinear elliptic equation with non-coercivity in divergentiel form in Orlicz spaces

2019 ◽  
Author(s):  
Aberqi Ahmed ◽  
Bennouna Jaouad ◽  
Elmassoudi Mhamed
Keyword(s):  
Elliptic Equation ◽  
Nonlinear Elliptic Equation ◽  
Orlicz Spaces ◽  
Nonlinear Elliptic

scholarly journals Abstract-valued Orlicz spaces of range-varying type

2018 ◽  
Vol 16 (1) ◽  
pp. 924-954 ◽  
Author(s):  
Qinghua Zhang
Keyword(s):  
Banach Space ◽  
Elliptic Equation ◽  
Differential Inclusion ◽  
Sobolev Spaces ◽  
Nonlinear Elliptic Equation ◽  
Orlicz Spaces ◽  
Convex Functional ◽  
Geometrical Properties ◽  
Nonstandard Growth ◽  
Nonlinear Elliptic

AbstractThis paper mainly deals with the abstract-valued Orlicz spaces of range-varying type. Using notions of Banach space net and continuous modular net etc., we give definitions of Lϱθ(⋅)(I, Xθ(⋅)) and $\begin{array}{} L_{+}^{\varrho_{\theta(\cdot)}} \end{array} $(I, Xθ(⋅)), and discuss their geometrical properties as well as the representation of $\begin{array}{} L_{+}^{\varrho_{\theta(\cdot)}} \end{array} $(I, Xθ(⋅))*. We also investigate some functionals and operators on Lϱθ(⋅)(I, Xθ(⋅)), giving expression for the subdifferential of the convex functional generated by another continuous modular net. After making some investigations on the Bochner-Sobolev spaces W1, ϱθ(⋅)(I, Xθ(⋅)) and $\begin{array}{} W_{\textrm{per}}^{1,\varrho_{\theta(\cdot)}} \end{array} $(I, Xθ(⋅)), and the intersection space $\begin{array}{} W_{\textrm{per}}^{1,\varrho_{\theta(\cdot)}} \end{array} $(I, Xθ(⋅)) ∩ Lφϑ(⋅)(I, Vϑ(⋅)), a second order differential inclusion together with an anisotropic nonlinear elliptic equation with nonstandard growth are also taken into account.

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.

Nonlinear Elliptic Equations in Strip-Like Domains

2012 ◽  
Vol 12 (4) ◽  
Author(s):  
Jaeyoung Byeon ◽  
Kazunaga Tanaka
Keyword(s):  
Elliptic Equation ◽  
Positive Solution ◽  
Bounded Domain ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equation ◽  
Nonlinear Elliptic Equations ◽  
Nonlinear Elliptic

AbstractWe study the existence of a positive solution of a nonlinear elliptic equationwhere k ≥ 2 and D is a bounded domain domain in R

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