## Abstract

The vector version of Krasnoselskii’s fixed point theorem in cones is used to obtain existence and localization results for the Dirichlet boundary value problem associated to second order ordinary differential systems with nonlinearities having different behaviors both in components and variables.

## Authors

**Radu Precup**

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

## Keywords

positive solution; differential system; boundary value problem; fixed point; cone.

## Paper coordinates

R. Precup, *Positive solutions of nonlinear systems via the vector version of Krasnoselskii’s fixed point theorem in cones*, Annals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity, 5 (2007), 129-138.

## About this paper

##### Journal

Annals of the Tiberiu Popoviciu Seminar

of Functional Equations, Approximation and Convexity

##### Publisher Name

##### DOI

##### Print ISSN

##### Online ISSN

1584-4536

google scholar link

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[2] M.A. Krasnoselskii, Fixed points of cone-compressing and cone-expanding operators, Soviet. Math. Dokl. 1 (1960), 1285-1288.

[3] D. O’Regan and R. Precup, Theorems of Leray-Schauder Type and Applications, Gordon and Breach, Amsterdam, 2001.

[4] A.I. Perov and A.V. Kibenko, O a certain general method for investigation of boundary value problems (Russian), Izv. Akad. Nauk SSSR 30 (1966), 249-264.

[5] R. Precup, Methods in Nonlinear Integral Equations, Kluwer, Dordrecht, 2002.

[6] R. Precup, A vector version of Krasnoselskii’s fixed point theorem in cones and positive periodic solutions of nonlinear systems, J. Fixed Point Theory Appl. 2 (2007), to appear.