Positive solutions of a nonlinear integral equation from biomathematics

• Autorzy: Trif T.
• Języki publikacji: EN

Abstrakty

EN

The aim of the present paper is to investigate the existence of positive continuous solutions of the nonlinear integral equation x(t) = St-r f(s, x(s))ds, arising in infectious diseases. We give sufficient conditions ensuring the existence of positive periodic continuous solutions of this equation, provided that f is a continuous function periodic in the first argument. We also study the existence of positive continuous solutions of the initial value problem for the considered equation.

Słowa kluczowe

EN

positive solution; nonlinear integral equation; biomathematics

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 1999
• Tom: Vol. 32, nr 1
• Strony: 129--138
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Trif T.

• Fac. De Matematicǎ Şi Informaticǎ, Universitatea Babeş-Bolyai, Str. Kogǎlniceanu Nr. 1, R0-3400 Cluj-Napoca, Romania

Bibliografia

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• [2] D. Guo and V. Lakshmikantham, Positive Solutions of Nonlinear Integral Equations Arising in Infectious Diseases, J. Math. Anal. Appl. 134 (1988), 1-8.
• [3] P. Hartman, Ordinary Differential Equations, John Wiley, New York 1964.
• [4] R. Precup, Positive solutions of the initial value problem for an integral equation modeling infectious disease, in: Seminar on Fixed Point Theory, Preprint Nr. 3,1. A. Rus (eds.), Babeş-Bolyai University, Cluj-Napoca (1991), 25-30.
• [5] R. Precup, Monotone technique to the initial value problem for a delay integral equation from biomathematics, Studia Univ. Babeş-Bolyai Math. 40 (1995), 63-73.
• [6] A. Stokes, The applications of a fixed point theorem to a variety of non-linear stability problems, in: Contributions to the theory of nonlinear oscillations, Vol. V, Princeton University Press, Princeton, N. J. (1960), 173-184.
• [7] L. R. Williams and R. W. Leggett, Nonzero solutions of nonlinear integral equations modeling infectious disease, SIAM J. Math. Anal. 13 (1982), 112-121.