Behavior properties and ordinary differential equations


The goal of this paper is to discuss the implications of the behavior properties from classical analysis (positivity, monotonicity, convexity, convexity of high order) [PE72], [PT44], [Pr85], into the qualitative theory of ordinary differential equations. We survey our own results concerning this subject in connection with other contributions in literature.


Radu Precup
Babes-Bolyai University, Cluj-Napoca, Romania



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R. Precup, Behavior properties and ordinary differential equations, Conference on Analysis, Functional Equations, Approximation and Convexity in Honour of Professor Elena Popoviciu, Cluj-Napoca, October 1999, 257-263.


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Conference on analysis Functional Equations Approximation and Convexity Cluj-Napoca

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[Pr94] R. Precup, Periodic solutions for an integral equation from biomathematics via Leray-Schauder principle, Studia Univ. Babes-Bolyai Math. 39 (1994), no.1., 47-58.
[Pr.95] R. Precup, Monotone technique to the initial values problem for a delay integral equation from biomathematics, Studia Univ. Babes-Bolyai Math. 40 (1995), no.2, 63-73.
[Pr96] R. Precup, Monotone iterations for decreasing maps in ordered Banach spaces, Proc. Sci, Comm., Meeting of  “Aurel Vlaicu” Univ., Arad, 1996, 105-108.
[Prap1[ R. Precup, Convexity and quadratic monotone approximation in delay differential equations, Rev. Anal. Numer. Theor. Approx., in print.
[Prap2] R. Precup, On the positivity of the green’s function of focal boundary value problems, to appear.
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