Bulletin of the Belgian Mathematical Society - Simon Stevin

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

Somayeh Saiedinezhad

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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

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1536631238

Digital Object Identifier
doi:10.36045/bbms/1536631238

Mathematical Reviews number (MathSciNet)
MR3852679

Zentralblatt MATH identifier
06970025

Subjects
Primary: 45M10: Stability theory 47H08: Measures of noncompactness and condensing mappings, K-set contractions, etc. 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 47H30: Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.) [See also 45Gxx, 45P05]

Keywords
Hölder space measure of noncompactness fixed point of Darbo type quadratic integral equation of Hammerstein type

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


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