Behavior properties and ordinary differential equations

Abstract


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.

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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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[Be65] R. Bellman and R. Kalaba, Quasiliniarization and Nonlinear Boundary Value Problems, American Elsevier, New York, 1965.
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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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