A strongly nonlinear elliptic problem in Orlicz-Sobolev spaces

1986 ◽  
pp. 455-462 ◽  
Author(s):  
Jean-Pierre Gossez
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Problem ◽  
Nonlinear Elliptic Problem ◽  
Strongly Nonlinear ◽  
Nonlinear Elliptic

scholarly journals Existence result for a nonlinear elliptic problem by topological degree in Sobolev spaces with variable exponent

2021 ◽  
Vol 7 (1) ◽  
pp. 50-65
Author(s):  
Mustapha Ait Hammou ◽  
Elhoussine Azroul
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Problem ◽  
Topological Degree ◽  
Variable Exponent ◽  
Existence Of Solutions ◽  
Nonlinear Elliptic Problem ◽  
Technical Approach ◽  
Nonlinear Elliptic ◽  
Variable Exponent Sobolev Spaces ◽  
Topological Degree Method

AbstractThe aim of this paper is to establish the existence of solutions for a nonlinear elliptic problem of the form\left\{ {\matrix{{A\left( u \right) = f} \hfill & {in} \hfill & \Omega \hfill \cr {u = 0} \hfill & {on} \hfill & {\partial \Omega } \hfill \cr } } \right.where A(u) = −diva(x, u, ∇u) is a Leray-Lions operator and f ∈ W−1,p′(.)(Ω) with p(x) ∈ (1, ∞). Our technical approach is based on topological degree method and the theory of variable exponent Sobolev spaces.

An existence theorem for a strongly nonlinear elliptic problem in Musielak–Orlicz spaces

2014 ◽  
Vol 41 (2) ◽  
pp. 175-184
Author(s):  
Abdelmoujib Benkirane ◽  
Fatimazahra Blali ◽  
Mohamed Sidi El Vally
Keyword(s):  
Existence Theorem ◽  
Elliptic Problem ◽  
Orlicz Spaces ◽  
Nonlinear Elliptic Problem ◽  
Strongly Nonlinear ◽  
Nonlinear Elliptic
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