Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 127, pp. 1-9.

Title: Positive solutions for a system of nonlinear
       boundary-value problems on time scales

Author: A. Kameswara Rao (Andhra Univ. Visakhapatnam, India)

Abstract:
 We determine the values of a parameter $\lambda$ for which there
 exist positive solutions to the system of dynamic equations
 $$\displaylines{
 u^{\Delta \Delta}(t)+\lambda p(t)f(v(\sigma(t)))=0,\quad 
  t\in[a, b]_\mathbb{T}, \cr
 v^{\Delta \Delta}(t)+\lambda q(t)g(u(\sigma(t)))=0,
 \quad t\in[a, b]_\mathbb{T},
 }$$
 with the  boundary conditions,
 $\alpha u(a)-\beta u^{\Delta}(a)=0$,
 $\gamma u(\sigma^2(b))+\delta u^{\Delta}(\sigma(b))=0$,
 $\alpha v(a)-\beta v^{\Delta}(a)=0$,
 $\gamma v(\sigma^2(b))+\delta v^{\Delta}(\sigma(b))=0$, where
 $\mathbb{T}$ is a time scale. To this end we apply a Guo-Krasnosel'skii
 fixed point theorem.

Submitted July 6, 2009. Published October 04, 2009.
Math Subject Classifications: 39A10, 34B15, 34A40.
Key Words: Dynamic equations; eigenvalue intervals; 
           positive solution; cone.