JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (6): 101-108.doi: 10.6040/j.issn.1671-9352.0.2020.062

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Existence and uniqueness of solutions for a class of boundary value problems of nonlinear fourth-order ordinary differential equations

YANG Li-juan   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2020-06-01

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Abstract: This article considers the existence and uniqueness of solutions of boundary value problems of nonlinear fourth-order ordinary differential equations{u(4)(t)=f(t,u(t),u'(t),u″(t)), a.e. t∈(0,1),u(0)=u″(0)=u(1)=u″(1)=0,where nonlinearity f:［0,1］×R3→R is a Carathéodory function. The existence of solutions is obtained when f satisfies the condition of proper utmost linear growth by using the Leray-Schauder principle. Furthermore, the uniqueness of solutions is proved when f satisfies the Lipschitz condition.

Key words: Leray-Schauder principle, Wirtingers inequality, solution, existence, uniqueness

CLC Number: 

  • O175.8
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