%0 Journal Article
%T Multiple Positive Solutions for m-Point Boundary Value Problem on Time Scales
%A Jie Liu
%A Hong-Rui Sun
%J Boundary Value Problems
%D 2011
%I Springer
%R 10.1155/2011/591219
%X The purpose of this article is to establish the existence of multiple positive solutions of the dynamic equation on time scales ( (u¦¤(t))) +h(t)f(t,u(t),u¦¤(t))=0,  t¡Ê(0,T)T, subject to the multi-point boundary condition u¦¤(0)=0,  u(T)=¡Æi=1m 2aiu(¦Îi), where  : ¡ú  is an increasing homeomorphism and satisfies the relation  (xy)= (x) (y) for x,y¡Ê , which generalizes the usually p-Laplacian operator. An example applying the result is also presented. The main tool of this paper is a generalization of Leggett-Williams fixed point theorem, and the interesting points are that the nonlinearity f contains the first-order derivative explicitly and the operator   is not necessarily odd.
%U http://dx.doi.org/10.1155/2011/591219