T hree Solutions For A (p(x, .), q(x, .))—Kirchhof Type Elliptic System in General Fractional Sobolev Space With Variable Exponents
Minimax theory and its applications, Tome 10 (2025) no. 1
In this work, we introduce the general weighted fractional Sobolev spaces with variable exponents , ( , ) , ( ) s p x y K Wω and we prove their continuous and compact embeddings into weighted Lebesgue spaces with variable exponent (.)( ) Lγ ω . Moreover, we consider a class of fractional elliptic systems involving general (p(x,.), q(x,.))—Laplacian operators. Our main tool is based on the Three Critical Points Theorem introduced by B. Ricceri and on the theory of fractional Sobolev spaces with variable exponents.
Mots-clés :
Elliptic systems, General fractional Sobolev spaces, Nonlocal problem, General fractional p(x, .)- Laplacian, Kirchhoff type Problems, Three Critical Points Theorem
@article{MTA_2025_10_1_a9,
author = {Elhoussine Azroul and Athmane Boumazourh and Houria El-Yahyaoui},
title = {T hree {Solutions} {For} {A} (p(x, .), q(x, {.)){\textemdash}Kirchhof} {Type} {Elliptic} {System} in {General} {Fractional} {Sobolev} {Space} {With} {Variable} {Exponents}},
journal = {Minimax theory and its applications},
year = {2025},
volume = {10},
number = {1},
url = {http://geodesic.mathdoc.fr/item/MTA_2025_10_1_a9/}
}
TY - JOUR AU - Elhoussine Azroul AU - Athmane Boumazourh and Houria El-Yahyaoui TI - T hree Solutions For A (p(x, .), q(x, .))—Kirchhof Type Elliptic System in General Fractional Sobolev Space With Variable Exponents JO - Minimax theory and its applications PY - 2025 VL - 10 IS - 1 UR - http://geodesic.mathdoc.fr/item/MTA_2025_10_1_a9/ ID - MTA_2025_10_1_a9 ER -
%0 Journal Article %A Elhoussine Azroul %A Athmane Boumazourh and Houria El-Yahyaoui %T T hree Solutions For A (p(x, .), q(x, .))—Kirchhof Type Elliptic System in General Fractional Sobolev Space With Variable Exponents %J Minimax theory and its applications %D 2025 %V 10 %N 1 %U http://geodesic.mathdoc.fr/item/MTA_2025_10_1_a9/ %F MTA_2025_10_1_a9
Elhoussine Azroul; Athmane Boumazourh and Houria El-Yahyaoui. T hree Solutions For A (p(x, .), q(x, .))—Kirchhof Type Elliptic System in General Fractional Sobolev Space With Variable Exponents. Minimax theory and its applications, Tome 10 (2025) no. 1. http://geodesic.mathdoc.fr/item/MTA_2025_10_1_a9/