JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (7): 16-21.doi: 10.6040/j.issn.1671-9352.0.2019.788

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Existence and uniqueness of solutions for a class fourth-order periodic boundary value problems

WANG Tian-xiang, LI Yong-xiang*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2020-07-08

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Abstract: By using Leray-Schauder fixed point theorem, this paper discusses the existence and uniqueness of solutions for the fourth-order periodic boundary value problem{u(4)(t)=f(t,u(t),u'(t)), t∈［0,1］,u(i)(0)=u(i)(1), i=0,1,2,3,where f:［0,1］×R2→R continuous. existence and uniqueness of solutions is obtained under the inequality conditions that allow the nonlinear term f(t,x,y) to grow superlinearly on x and y.

Key words: fourth-order periodic boundary value problem, existence and uniqueness, superlinear growth, Leray-Schauder fixed point theorem

CLC Number: 

  • O175.8
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