Existence and Uniqueness of Solutions to Boundary Value Problems of a Class of Nonlinear 3rd-Order Differential Equations

YANG Jingbao; MO Jiaqi

doi:10.21656/1000-0887.400158

Volume 41 Issue 2

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YANG Jingbao, MO Jiaqi. Existence and Uniqueness of Solutions to Boundary Value Problems of a Class of Nonlinear 3rd-Order Differential Equations[J]. Applied Mathematics and Mechanics, 2020, 41(2): 216-222. doi: 10.21656/1000-0887.400158

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Existence and Uniqueness of Solutions to Boundary Value Problems of a Class of Nonlinear 3rd-Order Differential Equations

doi: 10.21656/1000-0887.400158

YANG Jingbao¹,
MO Jiaqi²

¹Department of Education, Bozhou University, Bozhou, Anhui 236800, P.R.China;²School of Mathematics & Statistics, Anhui Normal University, Wuhu, Anhui 241003, P.R.China

Received Date: 2019-05-06
Rev Recd Date: 2019-05-10
Publish Date: 2020-02-01

Abstract

Abstract

The existence and uniqueness of solutions to the boundary value problem of a class of nonlinear 3rd-order differential equations were studied. Firstly, the results of the research on the boundary values of 3rd-order differential equations at home and abroad in recent years were combed. Then the boundary value problem of nonlinear 3rd-order differential equations with nonlinear boundary value conditions was put forth, and the solution to the related linear problem was explored. Finally, the Banach fixed point theorem was used to prove that the proposed boundary value problem has a unique solution. An example illustrates the applicability of the main results.
- Banach fixed point theorem,
- 3rd-order differential equation,
- 2-point boundary value problem

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References

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