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

Keyu Zhang; Yaohong Li; Jiafa Xu; Donal O’regan

doi:10.3934/math.2023458

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

Keyu Zhang
, Yaohong Li
, Jiafa Xu
, Donal O’regan

Mathematics

Qilu Normal University
Suzhou University
Chongqing Normal University

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

2 Citations (Scopus)

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).

Original language	English
Pages (from-to)	9146-9165
Number of pages	20
Journal	AIMS Mathematics
Volume	8
Issue number	4
DOIs	https://doi.org/10.3934/math.2023458
Publication status	Published - 2023

Keywords

extremal solutions
fourth-order differential equation
integral boundary value problem
nontrivial solutions
topological degree
upper-lower solution

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10.3934/math.2023458

Cite this

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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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AU - Xu, Jiafa

AU - O’regan, Donal

PY - 2023

Y1 - 2023

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AB - 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).

KW - extremal solutions

KW - fourth-order differential equation

KW - integral boundary value problem

KW - nontrivial solutions

KW - topological degree

KW - upper-lower solution

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ER -

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

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Keywords

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