Abstract
In this paper we investigate the existence of solutions to a kind of fourth-order impulsive differential equations with integral boundary value conditions. By employing the Schauder fixed point theorem, we obtain sufficient conditions which ensure the system has at lease one solution. Also by using the contraction mapping theorem we get the uniqueness result. Finally an example is given to illustrate the effectiveness of our results.
Highlights
Fourth-order boundary value problems have attached much attention from many authors; for example, see Sun and Wang [ ], Yao [ ], O’Regan [ ], Yang [ ], Zhang [ ], Gupta [ ], Agarwal [ ], Bonanno and Bella [ ], and Han and Xu [ ]
Sun and Xing Boundary Value Problems (2016) 2016:81 introduced and several new and more general results were obtained for the existence of at least single, double, or triple positive solutions
In Section, we show the existence and uniqueness of solutions to BVP ( . ) by the Schauder fixed point theorem and contraction mapping theorem
Summary
Fourth-order boundary value problems have attached much attention from many authors; for example, see Sun and Wang [ ], Yao [ ], O’Regan [ ], Yang [ ], Zhang [ ], Gupta [ ], Agarwal [ ], Bonanno and Bella [ ], and Han and Xu [ ]. In [ ], Zhang and Liu studied the following fourth-order four-point boundary value problem: By using the upper and lower solutions method, fixed point theorems, and the properties of the Green’s functions G(t, s) and H(t, s), the authors gave sufficient conditions for the existence of one positive solution. Zhou and Zhang [ ] employed a new existence theory to study the fourth-order p-Laplacian elasticity problems:
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
