The Method of Upper and Lower Solutions to Impulsive Differential Equation with Sturm–Liouville Integral Boundary Conditions

  • Huihui PangEmail author
  • Yuke Zhu
  • Mengyan Cui
Original Research


In this paper, we consider a second-order impulsive differential equation with Sturm–Liouville integral boundary conditions. We provide the sufficient conditions that guarantee the existence and multiplicity to our problem. Our technique is based on the method of upper and lower solutions and Leray–Schäuder degree theory. In the end, an example is worked out to illustrate our main results.


Impulsive differential equation Lower (upper)solution Integral boundary condition Leray–Schäuder degree 

Mathematics Subject Classification

34B10 34B15 


Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.


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Copyright information

© Foundation for Scientific Research and Technological Innovation 2018

Authors and Affiliations

  1. 1.College of ScienceChina Agricultural UniversityBeijingPeople’s Republic of China

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