Integrable solutions of a generalized mixed-type functional integral equation

الأصل · EN

In this work, we prove the existence of integrable solutions for the following generalized mixed-type nonlinear functional integral equation x(t)=g(t,(Tx)(t))+f(t,∫₀ᵗ k(t,s)u(t,s,(Qx)(s))ds),t∈[0,∞). Our result is established by means of a Krasnosel'skii type fixed point theorem proved in [M.A. Taoudi: Integrable solutions of a nonlinear functional integral equation on an unbounded interval, Nonlinear Anal. 71 (2009) 4131-4136]. In the last section we give an example to illustrate our result.