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.
Full Text
Article Information
| Title | Weak
solution for fractional $p(x)$-Laplacian problem with Dirichlet-type
boundary condition |
| Source | Methods Funct. Anal. Topology, Vol. 26 (2020), no. 3, 272-282 |
| DOI | 10.31392/MFAT-npu26_3.2020.08 |
| MathSciNet |
MR4165158 |
| Milestones | Received 14/06/2020; Revised 02/07/2020 |
| Copyright | The 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
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},
MRNUMBER = {MR4165158},
DOI = {10.31392/MFAT-npu26_3.2020.08},
URL = {https://mfat.imath.kiev.ua/article/?id=1399},
}
