POSITIVE SOLUTIONS FOR FRACTIONAL INTEGRAL BOUNDARY VALUE PROBLEM WITH DERIVATIVE DEPENDENCE

Changsong Shen; Xinan Hao

doi:10.1216/rmj.2023.53.1265

Abstract

We study the positive solutions for fractional integral boundary value problem with derivative dependence. Some properties of the associated Green function are established. By using the Guo–Krasnoselskii fixed-point theorem on cones, the existence results for positive solutions are obtained. Under certain monotone-type assumption on the nonlinearity, we establish the criteria of existence, multiplicity and nonexistence of positive solutions via the fixed-point index theory.

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Changsong Shen. Xinan Hao. "POSITIVE SOLUTIONS FOR FRACTIONAL INTEGRAL BOUNDARY VALUE PROBLEM WITH DERIVATIVE DEPENDENCE." Rocky Mountain J. Math. 53 (4) 1265 - 1283, August 2023. https://doi.org/10.1216/rmj.2023.53.1265

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Received: 30 August 2022; Revised: 5 September 2022; Accepted: 5 September 2022; Published: August 2023

First available in Project Euclid: 30 August 2023

MathSciNet: MR4635001

Digital Object Identifier: 10.1216/rmj.2023.53.1265

Subjects:

Primary: 34A08 , 34B10 , 34B18 , 34B27

Keywords: existence , fixed-point index , fractional integral boundary value problem , multiplicity , positive solution

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