JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (6): 93-100.doi: 10.6040/j.issn.1671-9352.0.2020.003

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Existence and uniqueness of solutions for a class of nonlinear fourth-order boundary value problem

LI Zhao-qian   

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

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Abstract: This paper is devoted to investigate the existence and uniqueness of solutions for a class of nonlinear fourth-order boundary value problem{u(4)(t)=f(t,u(t),u'(t),u″(t),u(t)), t∈(0,1),u(0)=u'(0)=u'(1)=u″(1)=0,where f:［0,1］×R4→R is a Carathéodory function. The existence of the solution is proved in the case f is utmost linear growth. Furthermore the existence and uniqueness of the solution is also obtained when f is Lipschitz type. The proof of the main results is based on Leray-Schauder fixed point theorem.

Key words: Carathéodory function, Wirtinger inequality, Leray-Schauder fixed point theorem, existence and uniqueness

CLC Number: 

  • O175.8
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