Local asymptotic attractivity for nonlinear quadratic functional integral equations
The paper deals with the quadratic functional-integral equation of mixed type \[ x(t)=[f(t,x(\alpha(t)))]\big(q(t)+\int_0^{\beta(t)}g(t,s,x(\gamma(s)))\,ds\big). \tag{1} \] Using a result about operator equations in Banach algebras, the author proves the existence of a solution of (1) in the space \(BC(\mathbb{R}_+,\mathbb{R})\). It is also proved that the solutions of (1) are uniformly locally asymptotically attractive on \(\mathbb{R}_+\).
uniformly locally asymptotically attractive solution
scientific article; zbMATH DE number 5509521
scientific article