The existence of positive solutions for high order fractional differential equations with sign changing nonlinearity and parameters

Luchao Zhang; Xiping Liu; Zhensheng Yu; Mei Jia; Luchao Zhang; Xiping Liu; Zhensheng Yu; Mei Jia

doi:10.3934/math.20231324

AIMS Mathematics

2023, Volume 8, Issue 11: 25990-26006. doi: 10.3934/math.20231324

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Research article

The existence of positive solutions for high order fractional differential equations with sign changing nonlinearity and parameters

College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Received: 15 June 2023 Revised: 17 July 2023 Accepted: 18 July 2023 Published: 08 September 2023
MSC : 34A08, 34A12, 34B18

By constructing an auxiliary boundary value problem, the difficulty caused by sign changing nonlinearity terms is overcome by means of the linear superposition principle. Using the Guo-Krasnosel'skii fixed point theorem, the results of the existence of positive solutions for boundary value problems of high order fractional differential equation are obtained in different parameter intervals under a more relaxed condition compared with the existing literature. As an application, we give two examples to illustrate our results.
- nonlinear fractional differential equations,
- Riemann-Liouville derivatives,
- boundary value problems,
- sign changing nonlinearity,
- positive solutions
Citation: Luchao Zhang, Xiping Liu, Zhensheng Yu, Mei Jia. The existence of positive solutions for high order fractional differential equations with sign changing nonlinearity and parameters[J]. AIMS Mathematics, 2023, 8(11): 25990-26006. doi: 10.3934/math.20231324

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Abstract

By constructing an auxiliary boundary value problem, the difficulty caused by sign changing nonlinearity terms is overcome by means of the linear superposition principle. Using the Guo-Krasnosel'skii fixed point theorem, the results of the existence of positive solutions for boundary value problems of high order fractional differential equation are obtained in different parameter intervals under a more relaxed condition compared with the existing literature. As an application, we give two examples to illustrate our results.

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