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Asymptotic behaviour of the iterates of nonnegative operators on Banach spaces with a cone

Socała J.

Bulletin of the Polish Academy of Sciences. Mathematics

2002

Vol. 50, no 2

179-187

An asymptotic convergence theorem for nonnegative operators on Banach spaces with a cone is proved. The general result is applied to a class of nonnegative operators on C^1 ([0, 1]).

Positive solutions of a nonlinear integral equation from biomathematics

Trif T.

Demonstratio Mathematica

1999

Vol. 32, nr 1

129-138

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.