Geodesic
Existence of positive solutions for nonlinear dynamic systems with a parameter on a measure chain
Electronic journal of differential equations, Tome 2007 (2007)
In this paper, we consider the following dynamic system with parameter on a measure chain

$\displaylines{ u^{\Delta\Delta}_{i}(t)+\lambda h_{i}(t)f_{i}(u_{1}(\sigma(t)), u_{2}(\sigma(t)),\dots ,u_{n}(\sigma(t)))=0,\quad t\in[a,b], \cr \alpha u_{i}(a)-\beta u^{\Delta}_{i}(a)=0,\quad \gamma u_{i}(\sigma(b))+\delta u^{\Delta}_{i}(\sigma(b))=0, }$

where $i=1,2,\dots ,n$. Using fixed-point index theory, we find sufficient conditions the existence of positive solutions.
Classification : 34B15, 39A10
Keywords: dynamic system, positive solution, cone, fixed point, measure chain 
@article{EJDE_2007__2007__a227,
     author = {Ma,  Shuang-Hong and Sun,  Jian-Ping and Wang,  Da-Bin},
     title = {Existence of positive solutions for nonlinear dynamic systems with a parameter on a measure chain},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1142.34321},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a227/}
}
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Ma,  Shuang-Hong; Sun,  Jian-Ping; Wang,  Da-Bin. Existence of positive solutions for nonlinear dynamic systems with a parameter on a measure chain. Electronic journal of differential equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a227/