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.
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania
positive solution; differential system; boundary value problem; fixed point; cone.
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.
Annals of the Tiberiu Popoviciu Seminar
of Functional Equations, Approximation and Convexity
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 R. Precup, Methods in Nonlinear Integral Equations, Kluwer, Dordrecht, 2002.
 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.