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...

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Main Authors: Xinguang Zhang, Peng Chen, Lishuang Li, Yonghong Wu
Format: Article
Language:English
Published: MDPI AG 2025-03-01
Series:Fractal and Fractional
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Online Access:https://www.mdpi.com/2504-3110/9/4/215
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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.
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issn 2504-3110
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publishDate 2025-03-01
publisher MDPI AG
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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