Posts by Radu Precup


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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[Be65] R. Bellman and R. Kalaba, Quasiliniarization and Nonlinear Boundary Value Problems, American Elsevier, New York, 1965.
[De85] K. Deimling, Nonlinear Functional Analysis, Springer, 1985.
[De98] S.G.Deo and C. McGloin Knoli, kth Order convergence of an iterative method for integro-differential equations, Nonlinear Stud. 5 (1998), 191-200.
[Kr64] M.A. Krasnoselskii, Positive solutions of operator equations, Noordhoff, Groningen, 1964.
[La85] G.S.Ladde, V. Lakshmikantham and A.S. Vatsala, Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman, Boston, 1985.
[La95] V. Lakshmikantham, S. Leela and S. Sivasundaram, Existensions of the method of quasiliniarization, J. Opt. Theory Appl. 87 (1995), 379-401.
[RePr] D. O’Regan and R.Precup, Theorems of Leray-Schauder Type an Applications, to appear.
[PE72] E. Popoviciu, Teoreme de medie din analiza matematica si legatura lor cu teoria interpolarii, Ed. Dacia, Cluj, 1972.
[PT44] T. Popoviciu, Les fonctions convexes, Herman Cie, Paris, 1944.
[Pr85] R. Precup, Behavior properties and some of their applications (Romanian) Ph. D. thesis,Univ. of Cluj, 1985.
[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.
[Pro67] H. Potter and H. Weinbeger, Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, 1967.
[Ra73] P.H. Rabinowitz, Branching of solutions of nonlinear equations, Rocky Mountain J. Math. 3 (1973), 161-202.
[Sch95] K. Schmitt, Positive solutions of semilinear elliptic boundary value problems, in: Topological Methods in Differential Equations and Inclusions (A., Granas and M.Frigon eds.), Kluwer, Dondrecht, 1995, 447-500.

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