Convexity and quadratic monotone approximation in delay differential equations


In this paper the method of quasiliniarization, an application of Newton’s method, recently generalized in [1], is used for the quadratic, monotonic, bilateral approximation of the solution of the delay problem (5). The result is applied to an integral equation from biomathematics.


Radu Precup
Babeş-Bolyai University, Department of Mathematics, Cluj-Napoca, Romania



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R. Precup, Convexity and quadratic monotone approximation in delay differential equations, Rev. Anal. Numér. Théor. Approx. 30 (2001), 89-93.


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Revue d’analyse numérique et de théorie d’approximation

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Academia Republicii S.R.

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[1] V. Lakshmikantham, S. Leela and S. Sivasundaram, Extensions of the method of quasilinearization, J. Optim. Theory Appl., 87 (1995), 379–401.
[2] L. C. Piccinini, G. Stampacchia and G. Vidossich, Ordinary Differential Equations in Rn, Springer-Verlag, Berlin, 1984.
[3] R. Precup, Positive solutions of the initial value problem for an integral equation modeling infectious disease, in Seminar on Fixed Point Theory: Preprint Nr. 3, 1991, University ”Babes-Bolyai”, Cluj, 1991, 25–30.
[4] R. Precup, Periodic solutions for an integral equation from biomathematics via Leray-Schauder principle, Studia Univ. Babes–Bolyai Math., 39 (1994), 47–58.
[5] R. Precup, Monotone technique to the initial values problem for a delay integral equation from biomathematics, Studia Univ. Babes–Bolyai Math., 40 (1995), 63–73.
[6] R. Precup and E. Kirr, Analysis of a nonlinear integral equation modelling infection diseases, in Proceedings of the International Conference, Timisoara 19–21 May 1997, 179–195.

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