Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 73, pp. 1-8.

Title: Existence of positive solutions for nonlinear dynamic
       systems with a parameter on a measure chain

Authors: Shuang-Hong Ma (Lanzhou Univ., Gansu, China)
         Jian-Ping Sun  (Lanzhou Univ., Gansu, China)
	 Da-Bin Wang    (Lanzhou Univ., Gansu, China)

Abstract:
 In this paper, we consider the following dynamic system with
 parameter on a measure chain $\mathbb{T}$,
 $$\displaylines{
 u^{\Delta\Delta}_{i}(t)+\lambda h_{i}(t)f_{i}(u_{1}(\sigma(t)),
 u_{2}(\sigma(t)),\dots ,u_{n}(\sigma(t)))=0,\quad
 t\in[a,b], \cr
 \alpha u_{i}(a)-\beta u^{\Delta}_{i}(a)=0,\quad
 \gamma u_{i}(\sigma(b))+\delta u^{\Delta}_{i}(\sigma(b))=0,
 }$$
 where $i=1,2,\dots ,n$. Using  fixed-point index theory, we find
 sufficient conditions the existence of positive solutions.
  
Submitted January 9, 2007. Published May 15, 2007.
Math Subject Classifications: 34B15, 39A10.
Key Words: Dynamic system; positive solution; cone; fixed point;
           measure chain.