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

Keyu Zhang; Yaohong Li; Jiafa Xu; Donal O'Regan; Keyu Zhang; Yaohong Li; Jiafa Xu; Donal O'Regan

doi:10.3934/math.2023458

AIMS Mathematics

2023, Volume 8, Issue 4: 9146-9165. doi: 10.3934/math.2023458

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

1.
School of Mathematics, Qilu Normal University, Jinan 250013, China
2.
School of Mathematics and Statistics, Suzhou University, Suzhou 234000, China
3.
School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
4.
School of Mathematical and Statistical Sciences, University of Galway, Galway, Ireland

Received: 27 December 2022 Revised: 05 February 2023 Accepted: 08 February 2023 Published: 13 February 2023
MSC : 34B10, 34B15, 34B18

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).
- fourth-order differential equation,
- integral boundary value problem,
- topological degree,
- upper-lower solution,
- nontrivial solutions,
- extremal solutions
Citation: Keyu Zhang, Yaohong Li, Jiafa Xu, Donal O'Regan. Nontrivial solutions for a fourth-order Riemann-Stieltjes integral boundary value problem[J]. AIMS Mathematics, 2023, 8(4): 9146-9165. doi: 10.3934/math.2023458

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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).

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