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

Josefa Caballero; Belén López; Kishin Sadarangani

doi:10.4171/zaa/1672

JournalszaaVol. 40, No. 1pp. 51–65

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

Josefa Caballero
Universidad de Las Palmas de Gran Canaria, Spain
Belén López
Universidad de Las Palmas de Gran Canaria, Spain
Kishin Sadarangani
Universidad de Las Palmas de Gran Canaria, Spain

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Abstract

In this work, we discuss the existence and uniqueness of positive solutions for the second order integral boundary value problem

⎩ ⎨ ⎧ x^{''} (t) + f (t, x (t), (H x) (t)) x (0) = 0, x (1) = 0, 0 < t < 1, = \int_{0}^{1} a (s) x (s) d s,

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.

Cite this article

Josefa Caballero, Belén López, Kishin Sadarangani, Existence and Uniqueness of Positive Solutions for a Singular Second-Order Integral Boundary Value Problem. Z. Anal. Anwend. 40 (2021), no. 1, pp. 51–65

DOI 10.4171/ZAA/1672