Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (6): 1592-1603.

• Articles • Previous Articles     Next Articles

Existence of Multiple Symmetric Positive Solutions of Higher Order Sturm-Liouville-type Boundary Value Problem

 PANG Hui-Hui1, ZHAO Jun-Fang2, GE Wei-Gao2   

  1. 1.College of Science, China Agricultural University, Beijing 100083;
    2.College of Science, Beijing Institute of Technology, Beijing 100081
  • Received:2008-08-07 Revised:2009-09-08 Online:2010-12-25 Published:2010-12-25
  • Supported by:

    中国农业大学科研启动基金(2009007)资助

Abstract:

In this paper, the authors consider the following higher order Sturm-Liouville-type four-point boundary value problem

{u(2m)(t)=f(t, u(t), u'(t), … , u{(2m-1)(t)),
 u{(2i)(0)-αu(2i+1)(ξ)=0, u(2i)}(1)+αu(2i+1)(η)=0, 0≤ i ≤ m-1, 
where nonlinear f depends on all lower order derivatives of u. Sufficient conditions of existence of at least three symmetric positive solutions are established by applying five-functional fixed point theorem.

Key words: Higher-order boundary value problem, Symmetric positive solution, Five-functional, Sturm-Liouville-type

CLC Number: 

  • 34B15
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