scholarly journals Nontrivial Solution for a Nonlocal Elliptic Transmission Problem in Variable Exponent Sobolev Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Bilal Cekic ◽  
Rabil A. Mashiyev
Keyword(s):  
Nontrivial Solution ◽  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Variable Exponent ◽  
Nonlinear Elliptic Equations ◽  
Transmission Problem ◽  
Variational Techniques ◽  
Nonlinear Elliptic ◽  
Variable Exponent Sobolev Spaces ◽  
Nonstandard Growth Condition

In this paper, by means of adequate variational techniques and the theory of the variable exponent Sobolev spaces, we show the existence of nontrivial solution for a transmission problem given by a system of two nonlinear elliptic equations ofp(x)-Kirchhoff type with nonstandard growth condition.

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.

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