
Global structure of the positive solution for a class of fourthorder boundary value problems with first derivative
 ZHANG Yali

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(8):
102110.
doi:10.6040/j.issn.16719352.0.2019.725

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This paper considers the global structure of positive solutions for a fourthorder 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.