scholarly journals Nonlinear elliptic problems in weighted variable exponent Sobolev spaces by topological degree

2019 ◽  
Vol 38 (4) ◽  
pp. 733-751
Author(s):  
Mustapha Ait Hammou ◽  
El Houssine Azroul
Keyword(s):  
Sobolev Spaces ◽  
Topological Degree ◽  
Variable Exponent ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic ◽  
Variable Exponent Sobolev Spaces ◽  
Weighted Variable

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.

scholarly journals On compact and bounded embedding in variable exponent Sobolev spaces and its applications

2019 ◽  
Vol 9 (2) ◽  
pp. 401-414
Author(s):  
Farman Mamedov ◽  
Sayali Mammadli ◽  
Yashar Shukurov
Keyword(s):  
Sobolev Space ◽  
Growth Condition ◽  
Sobolev Spaces ◽  
Variable Exponent ◽  
Lebesgue Spaces ◽  
Nonstandard Growth ◽  
Variable Exponent Sobolev Spaces ◽  
Nonstandard Growth Condition ◽  
Nonlinear Ode ◽  
Weighted Variable

Abstract For a weighted variable exponent Sobolev space, the compact and bounded embedding results are proved. For that, new boundedness and compact action properties are established for Hardy’s operator and its conjugate in weighted variable exponent Lebesgue spaces. Furthermore, the obtained results are applied to the existence of positive eigenfunctions for a concrete class of nonlinear ode with nonstandard growth condition.

scholarly journals On a nonlinear elliptic problems having large monotonocity with L1-data in weighted Orlicz-Sobolev spaces

2019 ◽  
Vol 5 (1) ◽  
pp. 104-116
Author(s):  
Badr El Haji ◽  
Mostafa El Moumni ◽  
Khaled Kouhaila
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Entropy Solution ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Equations ◽  
Monotonicity Condition ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic ◽  
Right Hand ◽  
L1 Data

AbstractWe prove in weighted Orlicz-Sobolev spaces, the existence of entropy solution for a class of nonlinear elliptic equations of Leray-Lions type, with large monotonicity condition and right hand side f ∈ L1(Ω).

scholarly journals Existence of entropy solutions for some nonlinear problems in Orlicz spaces

2002 ◽  
Vol 7 (2) ◽  
pp. 85-102 ◽  
Author(s):  
A. Benkirane ◽  
J. Bennouna
Keyword(s):  
Sobolev Spaces ◽  
Orlicz Spaces ◽  
Elliptic Problems ◽  
Nonlinear Problems ◽  
Entropy Solutions ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic

We study in the framework of Orlicz Sobolev spacesW01LM(Ω), the existence of entropic solutions to the nonlinear elliptic problems:−div a(x,u,∇u)+div Φ(u)=f in Ω, for the case where the second member of the equationf∈L 1(Ω), andΦ∈(C0(ℝ))N.

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.

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