## 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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