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Weak solution for fractional $p(x)$-Laplacian problem with Dirichlet-type boundary condition


Abstract

In the present paper, we prove the existence and uniqueness result of weak solutions to a class of fractional $p(x)$-Laplacian problem with Dirichlet-type boundary condition, the main tool used here is the varitional method combined with the theory of fractional Sobolev spaces with variable exponent.

Для одного класу задач із дробовим $p(x)$-лапласіаном з граничною умовою типу Дирихле доведено теорему про існування та єдиність слабкого розв'язку. Використовуються варіаційний метод і теорія дробових просторів Соболева змінного порядку.

Key words: Existence, fractional $p(x)$-Laplacian, uniqueness, variable exponent Sobolev fractional space, weak solution.


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Article Information

TitleWeak solution for fractional $p(x)$-Laplacian problem with Dirichlet-type boundary condition
SourceMethods Funct. Anal. Topology, Vol. 26 (2020), no. 3, 272-282
DOI10.31392/MFAT-npu26_3.2020.08
MilestonesReceived 14/06/2020; Revised 02/07/2020
CopyrightThe Author(s) 2020 (CC BY-SA)

Authors Information

Abdelali Sabri
EMAPI, Faculté des Sciences, Université Chouaib Doukkali, El Jadida, Morocco

Ahmed Jamea
EMAPI, Faculté des Sciences, Université Chouaib Doukkali, El Jadida, Morocco; Centre Régional des Métiers de l'Education et de la Formation Casablanca-Settat S.P. El Jadida, Morocco

Hamad Talibi Alaoui
EMAPI, Faculte des Sciences, Universite Chouaib Doukkali, El Jadida, Morocco


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Citation Example

Abdelali Sabri, Ahmed Jamea, and Hamad Talibi Alaoui, Weak solution for fractional $p(x)$-Laplacian problem with Dirichlet-type boundary condition, Methods Funct. Anal. Topology 26 (2020), no. 3, 272-282.


BibTex

@article {MFAT1399,
    AUTHOR = {Abdelali Sabri and Ahmed Jamea and Hamad Talibi Alaoui},
     TITLE = {Weak
  solution for fractional $p(x)$-Laplacian problem with Dirichlet-type
  boundary condition},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {26},
      YEAR = {2020},
    NUMBER = {3},
     PAGES = {272-282},
      ISSN = {1029-3531},
       DOI = {10.31392/MFAT-npu26_3.2020.08},
       URL = {http://mfat.imath.kiev.ua/article/?id=1399},
}


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