JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (12): 52-58.doi: 10.6040/j.issn.1671-9352.0.2021.191

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Existence, nonexistence and multiplicity of positive solutions for a class of nonlinear third order three point boundary value problems

ZHANG Rui-yan   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2021-11-25

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Abstract: This paper considers the existence, nonexistence and multiplicity of positive solutions for a class of nonlinear third-order three-point boundary value problems {u(t)+λf(t,u(t))=0, t∈［0,1］,u(0)=u'(0)=0, u'(1)=αu'(η),where λ>0 is a parameter, 0<η<1, 1<α<1/η, f:［0,1］×［0,∞)→(0,∞)is a continuous function. The proof of the main theorems is based on fixed point index theorems, Leray-Schauder degree and the method of upper and lower solutions.

Key words: third-order, multiplicity, existence, fixed-point index

CLC Number: 

  • O175.8
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