# 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.
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

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

?

## 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

1843 – 4401