Convexity and quadratic monotone approximation in delay differential equations

Authors

  • Radu Precup Babeş-Bolyai University, Cluj-Napoca

Abstract

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.

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References

V. Lakshmikantham, S. Leela and S. Sivasundaram, Extensions of the method of quasilinearization, J. Optim. Theory Appl., 87 (1995), 379-401, https://doi.org/10.1007/bf02192570

L. C. Piccinini, G. Stampacchia and G. Vidossich, Ordinary Differential Equations in Rⁿ, Springer-Verlag, Berlin, 1984.

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 "Babeş-Bolyai", Cluj, 1991, 25-30.

R. Precup, Periodic solutions for an integral equation from biomathematics via Leray-Schauder principle, Studia Univ. Babeş-Bolyai Math., 39 (1994), 47-58.

R. Precup, Monotone technique to the initial values problem for a delay integral equation from biomathematics, Studia Univ. Babeş-Bolyai Math., 40 (1995), 63-73.

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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Published

2001-02-01

How to Cite

Precup, R. (2001). Convexity and quadratic monotone approximation in delay differential equations. Rev. Anal. Numér. Théor. Approx., 30(1), 89–93. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2001-vol30-no1-art12

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