# Positive solutions of functional-differential systems via the vector version of Krasnoselskii’s fixed point theorem in cones

## 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.
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We study the existence of positive solutions of the functional-differential system

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$\left \{ \begin{array} [c]{c}% u_{1}^{\prime \prime}\left( t\right) +a_{1}\left( t\right) f_{1}\left( u_{1}(g(t\right) ),u_{2}\left( g\left( t\right) \right) )=0,\\ u_{2}^{\prime \prime}\left( t\right) +a_{2}\left( t\right) f_{2}% u_{1}\left( g\left( t\right) \right) ,u_{2}\left( g\left( t\right) \right) )=0, \end{array} \right.$

\((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

Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

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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

## PDF

##### Journal

Charpatian J. Math.

1584 – 2851

##### Online ISSN

1843 – 4401

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