JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (12): 47-53.doi: 10.6040/j.issn.1671-9352.0.2016.243

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Existence of positive solutions for a third-order three-point boundary value problem of nonlinear differential equations

GUO Li-jun   

  1. Department of Electro and Information Engineering, Lanzhou Jiaotong University Bowen College, Lanzhou 730101, Gansu, China
  • Received:2016-05-31 Online:2016-12-20 Published:2016-12-20

Abstract: The third order differential equation has a wide application background and an important theoretical value, Green function plays an important role in the existence of positive solutions for the third order three point boundary value problems. This paper is concerned with the following boundary value problem{u(t)+a(t)f(u(t))=0, t∈(0,1),u(0)=u″(0)=0, u'(1)=αu(η),where 0<η<1 and 0<α<1. By establishing Green function for the associated linear boundary value problem, the solution for the above boundary value problem is obtained. Then some existence criteria of at least two positive solutions are obtained by using the fixed point index theorem.

Key words: fixed point index theorem, existence, Green function, third-order three-point boundary value problem, cone, positive solution

CLC Number: 

  • O175.8
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