Opuscula Mathematica
Opuscula Math. 44, no. 2 (2024), 267-283

Positive solutions to a third order nonlocal boundary value problem with a parameter

Gabriela Szajnowska
Mirosława Zima
Abstract. We present some sufficient conditions for the existence of positive solutions to a third order differential equation subject to nonlocal boundary conditions. Our approach is based on the Krasnosel'skiĭ-Guo fixed point theorem in cones and the properties of the Green's function corresponding to the BVP under study. The main results are illustrated by suitable examples.
Keywords: boundary value problem, nonlocal boundary conditions, positive solution, cone.
Mathematics Subject Classification: 34B10, 34B15, 34B18, 34B27.
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About the authors ▼
Gabriela Szajnowska
https://orcid.org/0000-0002-5257-9435
University of Rzeszów, Institute of Mathematics, Pigonia 1, Rzeszów, 35-959, Poland
Mirosława Zima (corresponding author)
https://orcid.org/0000-0002-6152-4962
University of Rzeszów, Institute of Mathematics, Pigonia 1, Rzeszów, 35-959, Poland
About the article ▼
Communicated by Marek Galewski.
Received: 2023-07-19.
Revised: 2023-11-17.
Accepted: 2023-11-22.
Published online: 2024-01-15.
Cite this article as ▼
Gabriela Szajnowska, Mirosława Zima, Positive solutions to a third order nonlocal boundary value problem with a parameter, Opuscula Math. 44, no. 2 (2024), 267-283, https://doi.org/10.7494/OpMath.2024.44.2.267.
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