高阶Riemann-Liouville型分数阶脉冲微分方程积分边值问题的正解

数学物理学报 ›› 2023, Vol. 43 ›› Issue (1): 53-68.

高阶Riemann-Liouville型分数阶脉冲微分方程积分边值问题的正解

徐家发^*(),杨志春()

重庆师范大学数学科学学院重庆 401331

收稿日期:2021-12-09 修回日期:2022-10-17 出版日期:2023-02-26 发布日期:2023-03-07
通讯作者: ^*徐家发, E-mail: xujiafa292@sina.com
作者简介:杨志春, E-mail: yangzhch@126.com
基金资助:
国家自然科学基金项目(11971081);重庆市教育委员会科技研究重大项目(KJZD-M202000502)

Positive Solutions for a High Order Riemann-Liouville Type Fractional Impulsive Differential Equation Integral Boundary Value Problem

Xu Jiafa^*(),Yang Zhichun()

School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331

Received:2021-12-09 Revised:2022-10-17 Online:2023-02-26 Published:2023-03-07
Supported by:
The NSFC(11971081);Science and Technology Research Program of Chongqing Municipal Education Commission(KJZD-M202000502)

摘要/Abstract

摘要：

该文研究了具有半正非线性项和脉冲项的高阶Riemann-Liouville型分数阶脉冲微分方程积分边值问题. 利用不动点指数理论, 在超线性增长和次线性增长等条件下获得了该问题正解的存在性结论, 推广了近期这方面一些已有的成果.

关键词: 分数阶微分方程, 边值问题, 脉冲, 不动点指数, 正解

Abstract:

In this paper, we study a high order Riemann-Liouville type fractional impulsive differential equation integral boundary value problem involving semipositone the nonlinear and impulsive terms. By virtue of the fixed point index, we obtain the positive solutions theorems under some appropriate superlinear and sublinear growth conditions. The results here extend the existing study.

Key words: Fractional differential equations, Boundary value problems, Impulse, Fixed point index, Positive solutions

中图分类号:

O175.1

徐家发, 杨志春. 高阶Riemann-Liouville型分数阶脉冲微分方程积分边值问题的正解[J]. 数学物理学报, 2023, 43(1): 53-68.

Xu Jiafa, Yang Zhichun. Positive Solutions for a High Order Riemann-Liouville Type Fractional Impulsive Differential Equation Integral Boundary Value Problem[J]. Acta mathematica scientia,Series A, 2023, 43(1): 53-68.

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