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 ) , ∫ 0 t u ( t , s , x ( a ( s ) ) , x ( b ( s ) ) ) d s ) , ∀ 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.