Geodesic
Positive solutions for a system of nonlinear boundary-value problems on time scales
Electronic Journal of Differential Equations, Tome 2009 (2009).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 39A10, 34B15, 34A40
Keywords: dynamic equations, eigenvalue intervals, positive solution, cone 
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     author = {Rao, A.Kameswara},
     title = {Positive solutions for a system of nonlinear boundary-value problems on time scales},
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     year = {2009},
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Rao, A.Kameswara. Positive solutions for a system of nonlinear boundary-value problems on time scales. Electronic Journal of Differential Equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a158/