About the existence of integrable solutions of a functional-integral equation. (English) Zbl 0746.45004

Emmanuele, Giovanni

Rev. Mat. Univ. Complutense Madr. 4, No. 1, 65-69 (1991).

The author proves the existence of integrable solutions for a class of functional-integral equations of the type \(x(t)=g(t)+f\left(t,\int_ 0^ 1 k(t,s)x(\varphi(s))ds\right)\), \(t\in[0,1]\), which arises in different applications. He improves a previous result by J. Banaś and Z. Knap [Integrable solutions of a functional-integral equation, ibid. 2, No. 1, 31-38 (1989; Zbl 0679.45003)]. Basically, he deletes some kind of assumptions on the monotonicity of \(g\), \(f\) and \(k\). In the proof, the Tikhonov fixed point theorem is used.

Reviewer: A.Cañada (Granada)

MSC:

45G10	Other nonlinear integral equations
47J05	Equations involving nonlinear operators (general)

Keywords:

integrable solutions; functional-integral equations; Tikhonov fixed point theorem

Citations:

Zbl 0679.45003