Solvability and asymptotic stability of a nonlinear functional-integral equation

The aim of this work is to study the nonlinear functional-integral equation x(t)=f(t,x(t),∫0tu(t,s,x(a(s)),x(b(s)))ds),∀t∈R+. Using the technique of the measure of noncompactness and the Darbo fixed-point theorem, we prove the existence and asymptotic stability of solutions for the equation. A nontrivial example is given to support our result.