Triple positive solutions for some second-order boundary value problem on a measure chain

  • Authors:

  • Zhanbing Bai;Xiangqian Liang;Zengji Du

  • Affiliations:

  • Institute of Mathematics, Shandong University of Science and Technology, Qingdao 266510, People's Republic of China;Institute of Mathematics, Shandong University of Science and Technology, Qingdao 266510, People's Republic of China;Department of Mathematics, Xuzhou Normal University, Xuzhou, Jiangsu 221116, People's Republic of China

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2007

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Abstract

In this paper, we study the existence of three positive solutions for the second-order two-point boundary value problem on a measure chain, x^@D^@D(t)+p(t)f(t,x(@s(t)),x^@D(t))=0,t@?[t"1,t"2],a"1x(t"1)-a"2x^@D(t"1)=0,a"3x(@s(t"2))+a"4x^@D(@s(t"2))=0, where f:[t"1,@s(t"2)]x[0,~)xR-[0,~) is continuous and p:[t"1,@s(t"2)]-[0,~) a nonnegative function that is allowed to vanish on some subintervals of [t"1,@s(t"2)] of the measure chain. The method involves applications of a new fixed-point theorem due to Bai and Ge [Z.B. Bai, W.G. Ge, Existence of three positive solutions for some second order boundary-value problems, Comput. Math. Appl. 48 (2004) 699-707]. The emphasis is put on the nonlinear term f involved with the first order delta derivative x^@D(t).