Abstract
We study the existence of positive solutions of the functional-differential system
\(u_{1}^{\prime \prime}\left( t\right) +a_{1}\left( t\right) f_{1}\left(u_{1}(g(t\right) ),u_{2}\left( g\left( t\right) \right) )=0,\)
\(u_{2}^{\prime \prime}\left( t\right) +a_{2}\left( t\right) f_{2} u_{1}\left( g\left( t\right) \right) ,u_{2}\left( g\left( t\right)\right) )=0,\)
\((0<t<1)\), subject to linear boundary conditions. We prove the existence of at least one positive solution by using the vector version of Krasnoselskii’s
fixed point theorem in cones.
xxx
We study the existence of positive solutions of the functional-differential system
\bigskip%
\[
\left \{
\begin{array}
[c]{c}%
u_{1}^{\prime \prime}\left( t\right) +a_{1}\left( t\right) f_{1}\left(
u_{1}(g(t\right) ),u_{2}\left( g\left( t\right) \right) )=0,\\
u_{2}^{\prime \prime}\left( t\right) +a_{2}\left( t\right) f_{2}%
u_{1}\left( g\left( t\right) \right) ,u_{2}\left( g\left( t\right)
\right) )=0,
\end{array}
\right.
\]
\((0<t<1))\, subject to linear boundary conditions. We prove the existence of at
least one positive solution by using the vector version of Krasnoselskii’s
fixed point theorem in cones.
Authors
Sorin Budișan
”Babeș-Bolyai” University, Department of Mathematics, Cluj-Napoca, Romania
Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Keywords
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Paper coordinates
S. Budisan, R. Precup, Positive solutions of functional-differential systems via the vector version of Krasnoselskii’s fixed point theorem in cones, Carpathian J. Math. 27 (2011), 165-172, http://dx.doi.org/10.37193/CJM.2011.02.12
About this paper
Print ISSN
1584 – 2851
Online ISSN
1843 – 4401
google scholar link
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