JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (8): 102-110.doi: 10.6040/j.issn.1671-9352.0.2019.725

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Global structure of the positive solution for a class of fourth-order boundary value problems with first derivative

ZHANG Ya-li   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2020-07-14

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Abstract: This paper considers the global structure of positive solutions for a fourth-order boundary value problem with first derivative{u(4)(t)=rf(t,u(t),u'(t)), t∈(0,1),u(0)=u'(0)=u″(1)=u(1)=0,where r is a positive parameter, f:［0,1］×［0,∞)×［0,∞)→［0,∞)is continuous, and f(t,0,0)=0. When the parameter r changes in a certain range, the global structure of positive solutions of the problem are obtained by using the Rabinowitz global bifurcation theorems. The conclusions in this paper generalize and improve the related results.

Key words: fourth-order, positive solution, principal eigenvalue, bifurcation theorem

CLC Number: 

  • O175.8
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