Multiplicity of Positive Solutions for a Singular Tempered Fractional Initial-Boundary Value Problem with Changing-Sign Perturbation Term
In this paper, we focus on the multiplicity of positive solutions for a singular tempered fractional initial-boundary value problem with a <i>p</i>-Laplacian operator and a changing-sign perturbation term. By introducing a truncation function and combing with the properties of the soluti...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-03-01
|
| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/9/4/215 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850180370807390208 |
|---|---|
| author | Xinguang Zhang Peng Chen Lishuang Li Yonghong Wu |
| author_facet | Xinguang Zhang Peng Chen Lishuang Li Yonghong Wu |
| author_sort | Xinguang Zhang |
| collection | DOAJ |
| description | In this paper, we focus on the multiplicity of positive solutions for a singular tempered fractional initial-boundary value problem with a <i>p</i>-Laplacian operator and a changing-sign perturbation term. By introducing a truncation function and combing with the properties of the solution of isomorphic linear equations, we transform the changing-sign tempered fractional initial-boundary value problem into a positive problem, and then the existence results of multiple positive solutions are established by the fixed point theorem in a cone. It is worth noting that the changing-sign perturbation term only satisfies the weaker Carathèodory conditions, which implies that the perturbation term <i>ℏ</i> can be allowed to have an infinite number of singular points; moreover, the value of the changing-sign perturbation term can tend to negative infinity in some singular points. |
| format | Article |
| id | doaj-art-357712bbf9b148f09f66175b7bad6f8f |
| institution | OA Journals |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-357712bbf9b148f09f66175b7bad6f8f2025-08-20T02:18:11ZengMDPI AGFractal and Fractional2504-31102025-03-019421510.3390/fractalfract9040215Multiplicity of Positive Solutions for a Singular Tempered Fractional Initial-Boundary Value Problem with Changing-Sign Perturbation TermXinguang Zhang0Peng Chen1Lishuang Li2Yonghong Wu3School of Mathematical and Informational Sciences, Yantai University, Yantai 264005, ChinaSchool of Mathematical and Informational Sciences, Yantai University, Yantai 264005, ChinaSchool of Mathematical and Informational Sciences, Yantai University, Yantai 264005, ChinaDepartment of Mathematics and Statistics, Curtin University, Perth, WA 6845, AustraliaIn this paper, we focus on the multiplicity of positive solutions for a singular tempered fractional initial-boundary value problem with a <i>p</i>-Laplacian operator and a changing-sign perturbation term. By introducing a truncation function and combing with the properties of the solution of isomorphic linear equations, we transform the changing-sign tempered fractional initial-boundary value problem into a positive problem, and then the existence results of multiple positive solutions are established by the fixed point theorem in a cone. It is worth noting that the changing-sign perturbation term only satisfies the weaker Carathèodory conditions, which implies that the perturbation term <i>ℏ</i> can be allowed to have an infinite number of singular points; moreover, the value of the changing-sign perturbation term can tend to negative infinity in some singular points.https://www.mdpi.com/2504-3110/9/4/215multiplicityinitial-boundary value problemtempered fractional equationchanging-sign perturbation termsingularity<i>p</i>-Laplacian operator |
| spellingShingle | Xinguang Zhang Peng Chen Lishuang Li Yonghong Wu Multiplicity of Positive Solutions for a Singular Tempered Fractional Initial-Boundary Value Problem with Changing-Sign Perturbation Term Fractal and Fractional multiplicity initial-boundary value problem tempered fractional equation changing-sign perturbation term singularity <i>p</i>-Laplacian operator |
| title | Multiplicity of Positive Solutions for a Singular Tempered Fractional Initial-Boundary Value Problem with Changing-Sign Perturbation Term |
| title_full | Multiplicity of Positive Solutions for a Singular Tempered Fractional Initial-Boundary Value Problem with Changing-Sign Perturbation Term |
| title_fullStr | Multiplicity of Positive Solutions for a Singular Tempered Fractional Initial-Boundary Value Problem with Changing-Sign Perturbation Term |
| title_full_unstemmed | Multiplicity of Positive Solutions for a Singular Tempered Fractional Initial-Boundary Value Problem with Changing-Sign Perturbation Term |
| title_short | Multiplicity of Positive Solutions for a Singular Tempered Fractional Initial-Boundary Value Problem with Changing-Sign Perturbation Term |
| title_sort | multiplicity of positive solutions for a singular tempered fractional initial boundary value problem with changing sign perturbation term |
| topic | multiplicity initial-boundary value problem tempered fractional equation changing-sign perturbation term singularity <i>p</i>-Laplacian operator |
| url | https://www.mdpi.com/2504-3110/9/4/215 |
| work_keys_str_mv | AT xinguangzhang multiplicityofpositivesolutionsforasingulartemperedfractionalinitialboundaryvalueproblemwithchangingsignperturbationterm AT pengchen multiplicityofpositivesolutionsforasingulartemperedfractionalinitialboundaryvalueproblemwithchangingsignperturbationterm AT lishuangli multiplicityofpositivesolutionsforasingulartemperedfractionalinitialboundaryvalueproblemwithchangingsignperturbationterm AT yonghongwu multiplicityofpositivesolutionsforasingulartemperedfractionalinitialboundaryvalueproblemwithchangingsignperturbationterm |