Renormalized Solutions for the Non-local Equations in Fractional Musielak-Sobolev Spaces

被引：0
|
作者：
Li, Ying [1 ]
Zhang, Chao [2 ,3 ]
机构：
[1] Harbin Inst Technol, Sch Math, Harbin 150001, Peoples R China
[2] Harbin Inst Technol, Sch Math, Harbin 150001, Peoples R China
[3] Harbin Inst Technol, Inst Adv Study Math, Harbin 150001, Peoples R China
来源：
JOURNAL OF GEOMETRIC ANALYSIS | 2024年 / 34卷 / 12期
基金：
中国国家自然科学基金;
关键词：
Renormalized solutions; Existence; Uniqueness; L-1-data; Fractional Musielak-Sobolev spaces; PARABOLIC EQUATIONS; ELLIPTIC PROBLEMS; ORLICZ SPACES; EXISTENCE;
D O I：
10.1007/s12220-024-01835-y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the non-local equations with non-negative L-1-data in the fractional Musielak-Sobolev spaces. Utilizing approximation and energy methods, we establish the existence and uniqueness of non-negative renormalized solutions for such problems. The operators discussed in this work include the fractional Orlicz operators with variable exponents, the fractional double-phase operators with variable exponents, and the anisotropic fractional p-Laplacian operators, among others.
引用
收藏
页数：24
相关论文
共 50 条
  • [31] Multiplicity of solutions for non-local elliptic equations driven by the fractional Laplacian
    Wei, Yuanhong
    Su, Xifeng
    CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2015, 52 (1-2) : 95 - 124
  • [32] Multiplicity of solutions for non-local elliptic equations driven by the fractional Laplacian
    Yuanhong Wei
    Xifeng Su
    Calculus of Variations and Partial Differential Equations, 2015, 52 : 95 - 124
  • [33] A class of non-local elliptic system in non-reflexive fractional Orlicz-Sobolev spaces
    El-Houari, Hamza
    Chadli, Lalla Saadia
    Moussa, Hicham
    ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2023, 16 (07)
  • [34] PARABOLIC EQUATIONS IN MUSIELAK-ORLICZ-SOBOLEV SPACES
    Oubeid, M. L. Ahmed
    Benkirane, A.
    El Vally, M. Sidi
    INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS, 2014, 4 (02): : 174 - 191
  • [35] On topological degree for pseudomonotone operators in fractional Orlicz-Sobolev spaces: study of positive solutions of non-local elliptic problems
    H. El-Houari
    H. Sabiki
    H. Moussa
    Advances in Operator Theory, 2024, 9
  • [36] On topological degree for pseudomonotone operators in fractional Orlicz-Sobolev spaces: study of positive solutions of non-local elliptic problems
    El-Houari, H.
    Sabiki, H.
    Moussa, H.
    ADVANCES IN OPERATOR THEORY, 2024, 9 (02)
  • [37] Local boundedness of weak solutions to an inclusion problem in Musielak-Orlicz-Sobolev spaces
    Dong, Ge
    Fang, Xiaochun
    INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2024,
  • [38] Regularity in Lp Sobolev spaces of solutions to fractional heat equations
    Grubb, Gerd
    JOURNAL OF FUNCTIONAL ANALYSIS, 2018, 274 (09) : 2634 - 2660
  • [39] Eigenvalue type problem in s(., .)-fractional Musielak–Sobolev spaces
    Mohammed Srati
    Journal of Elliptic and Parabolic Equations, 2024, 10 : 387 - 413
  • [40] A bifurcation result for non-local fractional equations
    Bisci, Giovanni Molica
    Servadei, Raffaella
    ANALYSIS AND APPLICATIONS, 2015, 13 (04) : 371 - 394
12345