## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Existence and asymptotically stable solution of a Hammerstein type integral equation in a Hölder space

#### Abstract

The following nonlinear quadratic integral equation of Hammerstein type is studied. $$x(t)=p(t)+x(t)\int_0^{q(t)} H(t,\tau,x(\tau)){\rm d}\tau.$$ The methodology relies on the measure of noncompactness in the space of functions with tempered increments, namely the space of $\alpha$-Hölder continuous functions. The results follow from the Darbo fixed point theorem. Some examples are included to show the applicability of the main results.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 25, Number 3 (2018), 453-465.

Dates
First available in Project Euclid: 11 September 2018

https://projecteuclid.org/euclid.bbms/1536631238

Digital Object Identifier
doi:10.36045/bbms/1536631238

Mathematical Reviews number (MathSciNet)
MR3852679

Zentralblatt MATH identifier
06970025

#### Citation

Saiedinezhad, Somayeh. Existence and asymptotically stable solution of a Hammerstein type integral equation in a Hölder space. Bull. Belg. Math. Soc. Simon Stevin 25 (2018), no. 3, 453--465. doi:10.36045/bbms/1536631238. https://projecteuclid.org/euclid.bbms/1536631238