Acta mathematica scientia,Series A ›› 2003, Vol. 23 ›› Issue (2): 245-252.

• Articles • Previous Articles     Next Articles

Existence and Method of Lower and Upper Solutions for Fourth Order Nonlinear Boundary Value Problems

 LI Yong-Xiang   

  1. 西北师范大学数学系 兰州 730070
  • Online:2003-04-25 Published:2003-04-25
  • Supported by:

    甘肃省自然科学基金(ZS991A25007Z)、数学天元基金和西北师范大学科技 创新工程基金(NWNUKJCXGC212)资助项目

Abstract:

This paper studies the existence of solutions for the fou rthorder boundary value problem u^(4)(t) = f(t,u(t),u″(t)), t∈[0,1],u(0)=u(1)=u″(0)=u″(1)=0,where  f: [0,1]×R×R→R is  a  Carathéodory  function. In the general case without restriction for growth condition of f and assumption of monotonicity  on f, the author obtains the existence results of solution by using the met hod of lower and upper solutions. The validity  of finding solutions with the mo notone iterative method is also discussed.

Key words: Fourth order boundary value problem, Weak maximum princ iple, Second order integro differential equation, Lower and upper solution.

CLC Number: 

  • 34B15
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