BOUNDARY VALUE PROBLEMS FOR AN ITERATIVE DIFFERENTIAL EQUATION

Pingping Zhang; Wei Song

doi:10.11948/20230433

2024 Volume 14 Issue 4

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Pingping Zhang, Wei Song. BOUNDARY VALUE PROBLEMS FOR AN ITERATIVE DIFFERENTIAL EQUATION[J]. Journal of Applied Analysis & Computation, 2024, 14(4): 2431-2440. doi: 10.11948/20230433

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Pingping Zhang, Wei Song. BOUNDARY VALUE PROBLEMS FOR AN ITERATIVE DIFFERENTIAL EQUATION[J]. Journal of Applied Analysis & Computation, 2024, 14(4): 2431-2440. doi: 10.11948/20230433

BOUNDARY VALUE PROBLEMS FOR AN ITERATIVE DIFFERENTIAL EQUATION

Pingping Zhang^1,,
Wei Song^2, ,

1.
College of Science, Shandong University of Aeronautics, Binzhou 256600, Shandong, China
2.
College of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang, Guangdong 524088, China

Author Bio: Email: ppz.2005@163.com(P. Zhang)
Corresponding author: Email: dawenhxi@126.com (W. Song)
Fund Project: The authors were supported the Natural Science Foundation of Shandong Province (ZR2021MA044), Scientific Research Fund of Shandong University of Aeronautics (BZXYLG2118) and Scientific Research Start-up Funds of Guangdong Ocean University (060302102005)

Abstract

Abstract

This paper discusses the solutions of an iterative differential equation under general boundary value conditions. Using an auxiliary integral equation without the help of Green's functions usually being constructed in higher order equations, we prove the existence and uniqueness of solutions by the fixed point theorems of Schauder and Banach, respectively. Our theorems generalize and revise the related results.
- Existence /
- uniqueness /
- iterate /
- differential equation /
- fixed point theorems
MSC: 34B15, 34K10, 39B05

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References

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