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Zeitschrift für Analysis und ihre Anwendungen


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Volume 40, Issue 1, 2021, pp. 51–65
DOI: 10.4171/ZAA/1672

Published online: 2021-01-25

Existence and Uniqueness of Positive Solutions for a Singular Second-Order Integral Boundary Value Problem

Josefa Caballero[1], Belén López[2] and Kishin Sadarangani[3]

(1) Universidad de Las Palmas de Gran Canaria, Spain
(2) Universidad de Las Palmas de Gran Canaria, Spain
(3) Universidad de Las Palmas de Gran Canaria, Spain

In this work, we discuss the existence and uniqueness of positive solutions for the second order integral boundary value problem $$ \left\{ \begin{aligned} x''(t) + f(t,x(t),(Hx)(t)) &=0, \quad 0 < t < 1,\\ x(0)=0,\quad x(1)&= \int_{0}^{1}a(s)x(s)ds, \end{aligned} \right. $$ where the function $f$ has a singularity at $t_{0}=0$. Our main tool is a fixed point theorem of Wardowski (2012). Moreover, we present several examples illustrating our result.

Keywords: Integral boundary value problem, positive solution, fi xed point theorem

Caballero Josefa, López Belén, Sadarangani Kishin: Existence and Uniqueness of Positive Solutions for a Singular Second-Order Integral Boundary Value Problem. Z. Anal. Anwend. 40 (2021), 51-65. doi: 10.4171/ZAA/1672