On a perturbed functional integral equation of Urysohn type

Keywords: Functional integral equation Existence Monotonic solutions Urysohn Compact in measure a b s t r a c t We study the existence of monotonic solutions for a perturbed functional integral equation of Urysohn type in the space of Lebesgue integrable functions on an unbounded interval. The technique associated with measures of noncompactness (in both the weak and the strong sense) and the Darbo fixed point are the main tool to prove our main result. Nonlinear integral equations appear in many applications. For example, they occur in solving several problems arising in economics, engineering and physics. The most frequently investigated nonlinear integral equations are the Hammerstein integral equation and its generalization, the Urysohn integral equation (cf. [1–13]),