Acta mathematica scientia,Series A ›› 2004, Vol. 24 ›› Issue (3): 307-318.

• Articles • Previous Articles     Next Articles

Positive Solutions for Secondorder mPoint \=Boundary Value Problems of Robin Type

 MA Ru-Yun   

  • Online:2004-06-22 Published:2004-06-22
  • Supported by:

    国家自然科学基金(10271095)、 GG110107361003、 NWNUKJCXGC212 教育部重点科技项目和教育部优秀青年教师资助

Abstract:

Let a∈C[0,1], b∈C([0,1],(-∞, 0)).Let \-1(t) be the unique positive solution  of the linear problemu″+ a(t)u′+b(t)u=0 ,\=u′(0)=0, u(1)=1 .The author studies the existence of positive solutions for the nonhomogeneous mpoint boundary value problemu″+ a(t)u′+b(t)u+h(t)f(u)=0, \=u′(0)=0, u(1)-∑[DD(]m-2[]i=1[DD)]α\-i u(ξ\-i)=d,where d is a parameter, ξ\-i∈(0,1) and α\-i∈(0,∞)  are given constants satisfying∑[DD(]m-2[]i=1[DD)]α\-i\-1(ξ\-i) <1,i∈{1,\:,m-2}.Under suitable conditions, the author shows that there exists a positive number d\+* such that the problem has at least one positive solution for 0d\+*.

Key words: Multipoint boundary value problems, Positive solutions, Schauder fixed point theorem.

CLC Number: 

  • 34B10
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