Existence and uniqueness of positive solutions for a singular second-order integral boundary value problem
type: Item
instance of: scholarly article
title: Existence and uniqueness of positive solutions for a singular second-order integral boundary value problem
zbMATH Open document ID: 1481.34031
DOI: 10.4171/ZAA/1672
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2021-07-02T00:00:00Z
review text: Summary: In this work, we discuss the existence and uniqueness of positive solutions for the second order integral boundary value problem \[ \begin{cases} x''(t)+f(t,x(t),(Hx)(t))=0, \quad 0<t<1,\\ x(0)=0,\quad x(1)= \int_0^1a(s)x(s)ds, \end{cases} \] where the function \(f\) has a singularity at \(t_0=0\). Our main tool is a fixed point theorem of \textit{D. Wardowski} [Fixed Point Theory Appl. 2012, Paper No. 94, 6 p. (2012; Zbl 1310.54074)]. Moreover, we present several examples illustrating our result.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 7367446
zbMATH Keywords: integral boundary value problem
zbMATH Keywords: positive solution
zbMATH Keywords: fixed point theorem
author: J. Caballero
author: Belén López
author: K. Sadarangani
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7367446