Opuscula Math. 44, no. 2 (2024), 267-283
https://doi.org/10.7494/OpMath.2024.44.2.267
Opuscula Mathematica
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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- 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
- Communicated by Marek Galewski.
- Received: 2023-07-19.
- Revised: 2023-11-17.
- Accepted: 2023-11-22.
- Published online: 2024-01-15.
