JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (9): 35-41.doi: 10.6040/j.issn.1671-9352.0.2020.457

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Existence of positive solutions for a class of fourth-order boundary value problems with parameter

YANG Li-juan   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2021-09-13

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Abstract: This article studies the boundary value problems of fourth-order ordinary differential equations with parameter{u'(t)+au(t)+bu″(t)+cu'(t)+du(t)=rf(t,u(t),u″(t)), 01,u(0)=u(1)=u″(0)=u″(1)=0,where r is a positive parameter, a,b,c,d are constant coefficients, and the nonlinearity f: ［0,1］×［0,∞)×(-∞,0］→［0,∞) is a continuous function. When r is in a cetain range of values, the existence of positive solutions are obtained by using global bifurcation theorem.

Key words: fourth-order ODE, positive solution, bifurcation theorem, Krein-Rutman theorem

CLC Number: 

  • O175.14
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