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

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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  • Communicated by Marek Galewski.
  • Received: 2023-07-19.
  • Revised: 2023-11-17.
  • Accepted: 2023-11-22.
  • Published online: 2024-01-15.
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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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