Positive solutions of nonlinear integral equations arising in infectious diseases
The following nonlinear integral equation (1) \(x(t)=\int^{t}_{t- \tau}f(s,x(s))ds\) can be interpreted as a model for the spread of certain infectious diseases. This equation is examined in the heading under the assumptions that f(t,x) is nonnegative and continuous on the set \(R\times R_+\), is \(\omega\)-periodic in t and such that \(f(t,0)=0\) for \(t\in R\). Under some additional assumptions the equation (1) is proved to have at least two nontrivial, nonnegative, continuous and \(\omega\)-periodic solutions. A result on the convergence of the sequence of successive approximations is also established. A few examples illustrate the applicability of results obtained in this interesting paper.
scientific article; zbMATH DE number 4075790