JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (6): 42-48.doi: 10.6040/j.issn.1671-9352.0.2015.434

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Existence of multiple of solutions of first order multi-point boundary value problem

ZHU Wen-wen   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2015-09-14 Online:2016-06-20 Published:2016-06-15

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Abstract: We use the method of the upper and lower solutions and topological degree theory to study existence of multiple solutions of first order differential equations multi-point boundary value problem{u'(t)=f(t,u(t)), t∈［0,T］,u(0)+∑mk=1aku(tk)=cwhere c∈R, tk(k=1,2,3,…,m)satisfy 012<…mk<0 are constants, and 1+∑mk=1ak>0, f∈C(［0,T］×R, R). Finally, an example is presented to illustrate the application of the obtained result.

Key words: topological degree theory, multi-point boundary value problem, upper and lower solutions

CLC Number: 

  • O175.8
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