Existence results for a class of nonlinear singular $ p $-Laplacian Hadamard fractional differential equations

Limin Guo; Weihua Wang; Cheng Li; Jingbo Zhao; Dandan Min; Limin Guo; Weihua Wang; Cheng Li; Jingbo Zhao; Dandan Min

doi:10.3934/era.2024045

Electronic Research Archive

2024, Volume 32, Issue 2: 928-944. doi: 10.3934/era.2024045

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Research article

Existence results for a class of nonlinear singular $ p $-Laplacian Hadamard fractional differential equations

1.
School of Science, Changzhou Institute of Technology, Changzhou 213002, China
2.
School of Computer Science and Information Engineering, Changzhou Institute of Technology, Changzhou 213002, China
3.
School of Automotive Engineering, Changzhou Institute of Technology, Changzhou 213002, China
4.
Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 611756, China
5.
College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China

Received: 17 October 2023 Revised: 18 December 2023 Accepted: 02 January 2024 Published: 16 January 2024

Based on properties of Green's function and the some conditions of $ f(t, u) $, we found a minimal and a maximal positive solution by the method of sequence approximation. Moreover, based on the properties of Green's function and fixed point index theorem, the existence of multiple positive solutions for a singular $ p $-Laplacian fractional differential equation with infinite-point boundary conditions was obtained and, at last, an example was given to demonstrate the validity of our main results.
- Hadamard fractional differential equation,
- multiple positive solutions,
- infinite-point,
- minimal and maximal positive solutions
Citation: Limin Guo, Weihua Wang, Cheng Li, Jingbo Zhao, Dandan Min. Existence results for a class of nonlinear singular $ p $-Laplacian Hadamard fractional differential equations[J]. Electronic Research Archive, 2024, 32(2): 928-944. doi: 10.3934/era.2024045

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Abstract

Based on properties of Green's function and the some conditions of $ f(t, u) $, we found a minimal and a maximal positive solution by the method of sequence approximation. Moreover, based on the properties of Green's function and fixed point index theorem, the existence of multiple positive solutions for a singular $ p $-Laplacian fractional differential equation with infinite-point boundary conditions was obtained and, at last, an example was given to demonstrate the validity of our main results.

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