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Summer 2021 Multiplicity results to nonlinear Hammerstein integral equations and applications
Abdeljabbar Ghanmi, Samah Horrigue, Ziheng Zhang
J. Integral Equations Applications 33(2): 237-246 (Summer 2021). DOI: 10.1216/jie.2021.33.237

Abstract

Under certain assumptions on the functions f, G and h, we establish one new criterion on the operator L defined on C(I) by

Lu(t)=0wG(t,s)h(s)f(u(s))ds,tI,ω{1,},

to guarantee that the operator equation has at least three solutions, where I=[0,1] if ω=1 and I=[0,) if ω=, via the Leguette–Williams fixed point theorem. Two examples are given to demonstrate our main result.

Citation

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Abdeljabbar Ghanmi. Samah Horrigue. Ziheng Zhang. "Multiplicity results to nonlinear Hammerstein integral equations and applications." J. Integral Equations Applications 33 (2) 237 - 246, Summer 2021. https://doi.org/10.1216/jie.2021.33.237

Information

Received: 17 September 2019; Revised: 23 September 2020; Accepted: 8 October 2020; Published: Summer 2021
First available in Project Euclid: 31 August 2021

Digital Object Identifier: 10.1216/jie.2021.33.237

Subjects:
Primary: 34B15
Secondary: 37C25, 45G10

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.33 • No. 2 • Summer 2021
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