JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (12): 32-37.doi: 10.6040/j.issn.1671-9352.0.2019.320

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Monotone positive solutions of fourth-order boundary value problems with integral boundary conditions

HE Yan-qin, HAN Xiao-ling*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2019-12-11

Abstract: By using the monotone iterative technique, this article studies the existence of monotone positive solutions for fourth order boundary value problems with integral boundary conditions{u(4)(t)=f(t,u(t),u'(t)), t∈(0,1),u(0)=u'(1)=u(1)=0,u″(0)=∫10g(t)u″(t)dt,where f:[0,1]×[0,+∞)2→[0,+∞) is continuous, g:[0,1]→[0,+∞) is continuous, not only the existence of the positive solution of the problem is obtained, but also the initial value of the iterative sequence is a simple zero function or a primary function.

Key words: fourth-order boundary value problem, integral boundary condition, monotone positive solution, existence, iterative technique

CLC Number: 

  • O175.8
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