JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (2): 75-83.doi: 10.6040/j.issn.1671-9352.0.2020.289

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Existence of solutions for singular fourth-order m-point boundary value problems

WU Ruo-fei   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Online:2021-02-20 Published:2021-01-21

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Abstract: This article considers the existence of positive solutions for the singular fourth-order m-point boundary value problems {u(4)(t)=f(t,u(t),u'(t)), a.e. t∈(0,1),u'(0)=0, u(1)=∑m-2i=1aiu(ξi),u(0)=0, u″(1)=∑m-2i=1aiu″(ξi)where ξi∈(0,1), i=1,2,…,m-2, 0<ξ1<ξ2<…<ξm-2<1, ai∈R and ∑m-2i=1ai≠1. By using the fixed point theorem of Leray-Schauder and under some suitable assumptions of f, the existence of solutions is obtained. Note that nonlinear term f has some suitable singularities at t=1.

Key words: singularity, existence, multipoint, fixed point theorem of Leray-Schauder

CLC Number: 

  • O175.8
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