UNIQUE EXISTENCE RESULTS AND NUMERICAL SOLUTIONS FOR FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

Hui Wang; Lingling Zhang; Xiaoqiang Wang

doi:10.11948/20180158

2019 Volume 9 Issue 5

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Hui Wang, Lingling Zhang, Xiaoqiang Wang. UNIQUE EXISTENCE RESULTS AND NUMERICAL SOLUTIONS FOR FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2019, 9(5): 1639-1662. doi: 10.11948/20180158

Citation:

Hui Wang, Lingling Zhang, Xiaoqiang Wang. UNIQUE EXISTENCE RESULTS AND NUMERICAL SOLUTIONS FOR FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2019, 9(5): 1639-1662. doi: 10.11948/20180158

UNIQUE EXISTENCE RESULTS AND NUMERICAL SOLUTIONS FOR FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

1.
College of Mathematics, Taiyuan University of Technology, Yingze west Road, 030024, China
2.
State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Zhongguancun South Street, Beijing, China
3.
Department of Scientific Computing, Florida State University, Tallahassee, FL, 32306, USA

Corresponding author: Email address:tyutzll@126.com(L. Zhang)

Abstract

Abstract

The work is concerned with three kinds of fourth-order impulsive differential equations with nonlinear boundary conditions. We at first focused on studying the existence and uniqueness of positive solutions for these kinds of problems. By converting the problem to an equivalent integral equation, then applying the new class of fixed point theorems for the sum operator on cone, we obtain the sufficient conditions which not only guarantee the existence of a unique positive solution, but also be applied to construct two iterative sequences for approximating it. Further, we present the numerical methods for solving the fourth-order differential equations. At last, some examples are given with numerical verifications to illustrate the main results.
- Existence and uniqueness /
- positive solution /
- impulsive differential equations /
- fixed point theorem for sum operator /
- numerical solution
MSC: 34B15, 34B18, 34B37

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References

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