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Research Article | Open Access

Nontrivial solutions for a fourth-order Riemann-Stieltjes integral boundary value problem

Keyu Zhang1, Yaohong Li2, Jiafa Xu3( ), Donal O'Regan4
School of Mathematics, Qilu Normal University, Jinan 250013, China
School of Mathematics and Statistics, Suzhou University, Suzhou 234000, China
School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
School of Mathematical and Statistical Sciences, University of Galway, Galway, Ireland
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Abstract

In this paper we study a fourth-order differential equation with Riemann-Stieltjes integral boundary conditions. We consider two cases, namely when the nonlinearity satisfies superlinear growth conditions (we use topological degree to obtain an existence theorem on nontrivial solutions), when the nonlinearity satisfies a one-sided Lipschitz condition (we use the method of upper-lower solutions to obtain extremal solutions).

Keywords

fourth-order differential equationintegral boundary value problemtopological degreeupper-lower solutionnontrivial solutionsextremal solutions
CLC number: 34B10, 34B15, 34B18

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AIMS Mathematics
Volume 8 Issue 4,
April 2023
Pages 9146-9165
DOI: 10.3934/math.2023458

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Cite this article:
Zhang K, Li Y, Xu J, et al. Nontrivial solutions for a fourth-order Riemann-Stieltjes integral boundary value problem. AIMS Mathematics, 2023, 8(4): 9146-9165. https://doi.org/10.3934/math.2023458

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Received: 27 December 2022
Revised: 05 February 2023
Accepted: 08 February 2023
Published: 15 April 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)