The Existence of Positive Solutions for a <i>p</i>-Laplacian Tempered Fractional Diffusion Equation Using the Riemann–Stieltjes Integral Boundary Condition
In this paper, we focus on the existence of positive solutions for a class of <i>p</i>-Laplacian tempered fractional diffusion equations involving a lower tempered integral operator and a Riemann–Stieltjes integral boundary condition. By introducing certain new local growth conditions an...
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MDPI AG
2025-02-01
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| author | Lishuang Li Xinguang Zhang Peng Chen Yonghong Wu |
| author_facet | Lishuang Li Xinguang Zhang Peng Chen Yonghong Wu |
| author_sort | Lishuang Li |
| collection | DOAJ |
| description | In this paper, we focus on the existence of positive solutions for a class of <i>p</i>-Laplacian tempered fractional diffusion equations involving a lower tempered integral operator and a Riemann–Stieltjes integral boundary condition. By introducing certain new local growth conditions and establishing an a priori estimate for the Green’s function, several sufficient conditions on the existence of positive solutions for the equation are derived by using a fixed point theorem. Interesting points are that the tempered fractional diffusion equation contains a lower tempered integral operator and that the boundary condition involves the Riemann–Stieltjes integral, which can be a changing-sign measure. |
| format | Article |
| id | doaj-art-6bff2ec0b5ee411283313d45ccfea770 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-6bff2ec0b5ee411283313d45ccfea7702025-08-20T02:48:03ZengMDPI AGMathematics2227-73902025-02-0113354110.3390/math13030541The Existence of Positive Solutions for a <i>p</i>-Laplacian Tempered Fractional Diffusion Equation Using the Riemann–Stieltjes Integral Boundary ConditionLishuang Li0Xinguang Zhang1Peng Chen2Yonghong 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 existence of positive solutions for a class of <i>p</i>-Laplacian tempered fractional diffusion equations involving a lower tempered integral operator and a Riemann–Stieltjes integral boundary condition. By introducing certain new local growth conditions and establishing an a priori estimate for the Green’s function, several sufficient conditions on the existence of positive solutions for the equation are derived by using a fixed point theorem. Interesting points are that the tempered fractional diffusion equation contains a lower tempered integral operator and that the boundary condition involves the Riemann–Stieltjes integral, which can be a changing-sign measure.https://www.mdpi.com/2227-7390/13/3/541tempered fractional equationsRiemann–Stieltjes integralfixed point theorempositive solutionsp-Laplacian operator |
| spellingShingle | Lishuang Li Xinguang Zhang Peng Chen Yonghong Wu The Existence of Positive Solutions for a <i>p</i>-Laplacian Tempered Fractional Diffusion Equation Using the Riemann–Stieltjes Integral Boundary Condition Mathematics tempered fractional equations Riemann–Stieltjes integral fixed point theorem positive solutions p-Laplacian operator |
| title | The Existence of Positive Solutions for a <i>p</i>-Laplacian Tempered Fractional Diffusion Equation Using the Riemann–Stieltjes Integral Boundary Condition |
| title_full | The Existence of Positive Solutions for a <i>p</i>-Laplacian Tempered Fractional Diffusion Equation Using the Riemann–Stieltjes Integral Boundary Condition |
| title_fullStr | The Existence of Positive Solutions for a <i>p</i>-Laplacian Tempered Fractional Diffusion Equation Using the Riemann–Stieltjes Integral Boundary Condition |
| title_full_unstemmed | The Existence of Positive Solutions for a <i>p</i>-Laplacian Tempered Fractional Diffusion Equation Using the Riemann–Stieltjes Integral Boundary Condition |
| title_short | The Existence of Positive Solutions for a <i>p</i>-Laplacian Tempered Fractional Diffusion Equation Using the Riemann–Stieltjes Integral Boundary Condition |
| title_sort | existence of positive solutions for a i p i laplacian tempered fractional diffusion equation using the riemann stieltjes integral boundary condition |
| topic | tempered fractional equations Riemann–Stieltjes integral fixed point theorem positive solutions p-Laplacian operator |
| url | https://www.mdpi.com/2227-7390/13/3/541 |
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