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

Rao, A.Kameswara

Electronic journal of differential equations, Tome 2009 (2009)

Résumé

We determine the values of a parameter

$\displaylines{ u^{\Delta \Delta}(t)+\lambda p(t)f(v(\sigma(t)))=0,\quad t\in[a, b]_\mathbb{T}, \cr v^{\Delta \Delta}(t)+\lambda q(t)g(u(\sigma(t)))=0, \quad t\in[a, b]_\mathbb{T}, }$

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.

Détail

Classification : 39A10, 34B15, 34A40
Keywords: dynamic equations, eigenvalue intervals, positive solution, cone