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.

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

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About this paper

Journal

Charpatian J. Math.

Publisher Name
Print ISSN

1584 – 2851

Online ISSN

1843 – 4401

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