## Abstract

The paper deals with periodic solutions for an integral equation from biomathematics, via the Leray-Schauder principle.

The results obtained here refer to the existence, the uniqueness and monotone-iterative approximation of the nontrivial periodic solutions of the integral equation

\[

x(t)=\int_{-t}^t f(s,x(s))ds

\]

The proofs are based on the continuation Leray-Schauder principle and on the monotone iterations technique.

## Authors

**Radu Precup**

Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania

## Keywords

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## Paper coordinates

R. Precup, *Periodic solutions for an integral equation from biomathematics via Leray-Schauder principle*, Studia Univ. Babeş-Bolyai Math. 39 (1994) no. 1, 47-58.

## About this paper

##### Journal

Studia Universitatis Babes-Bolyai Mathematica

##### Publisher Name

??

##### DOI

##### Print ISSN

??

##### Online ISSN

MR: 98c:45019a.

google scholar link

[1] B.N.Busenberg, K.L. Cooke, Periodic solutions to delay differential equaitons arising in some models of epidemics, In: Applied Nonlinear Analysis@ (V. Lakshmikantham, Ed.), pp. 67-78, Academic Press, 1979.

[2] K.L. Cooke, J.L. Kaplan, A periodicity threshold theorem for epidemics and population growth, Math. Bioaciences 31(1976), 87-104.

[3] K. Deimling, “Nonlinear Functional Analysis”, Springer-Verlag, 1985.

[4] D. Guo, V. Lakshmikantham, Positiv e solutions of nonlinear integral equations arising in infections diseases, J. Math. Anal.Appl. 134(1988), 1-8.

[5] D. Guo, V. Lakshmikantham, “Nonlinear Problems in Abstract Cones”, Academic Press, Boston 1988.

[6] R.W.Leggett, L.R. Williams, A fixed point theorem with applications to an infections disease model, J. Math. Anal. Appl. 76(1980), 91-97.

[7] R. Precup, Positive solutions of the initial value problem for an integral equation modeling infections diseases, In “Seminar on Fixed Point Theory: Preprint Nr. 3, 1991” (I.A. Rus, Ed.), pp. 25-30, Babes-Bolyai University, Cluj, 1991.

[8] R. Precup, Monotone technique to the initial values problem for a delay integral equation from biomathematics, In “Itinerant Seminar on Functional Equations, Approximation and Convexity: Preprint Nr.6, 1993” (E. Popoviciu, Ed.), Babes-Bolyai University, Cluj, in press.

[9] I.A. Rus, A delay integral equation from biomathematics, in “Seminar on Differential Equations: Preprint Nr.3, 1989” (I.A. Rus, Ed.), pp. 87-90, Babes-Bolyai University, Cluj, 1989.

[10] H.L. Smith, On periodic solutions of a delay integral equation modelling epidemics, J. Math. Biol. 4(1977), 69-80.

[11] L.R. Williams, R.W. Leggett, Nonzero solutions of nonlinear integral equations modeling infections disease, SIAM J. Math. Anal. 13(1982), 112-121.