Existence of positive solutions of nonlinear m-point BVP for an increasing homeomorphism and positive homomorphism on time scales

  • Authors:

  • Wei Han;Zhen Jin;Shugui Kang

  • Affiliations:

  • Department of Mathematics, North University of China, Taiyuan Shanxi, 030051, PR China;Department of Mathematics, North University of China, Taiyuan Shanxi, 030051, PR China;College of Mathematics and Computer Science, Shanxi Datong University, Datong, Shanxi 037009, PR China

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2009

Quantified Score

Hi-index 7.29

Visualization

Abstract

In this paper, we will consider the following multipoint boundary value problem for the following second-order dynamic equations on time scales (@f(u^@D))^@?+a(t)f(t,u(t))=0,t@?(0,T),u(0)=@?i=1m-2a"iu(@x"i),@f(u^@D(T))=@?i=1m-2b"i@f(u^@D(@x"i)), where @f:R@?R is an increasing homeomorphism and positive homomorphism and @f(0)=0. By using fixed point theorems, we obtain an existence theorem of positive solutions for the above boundary value problem, which includes and improve some related results in the relevant literature. As an application, an example to demonstrate our results is given.