Title: Existence of positive solutions for a fourth-order differential equation with p-Laplacian and Riemann-Stieltjes integral boundary conditions

Authors: Yingqiu Wang; Dehong Ji

Addresses: School of Science, Tianjin University of Technology, Tianjin, 300384, China ' School of Science, Tianjin University of Technology, Tianjin, 300384, China

Abstract: This paper investigates a problem concerning the positive solutions for a fourth-order differential equation with p-Laplacian and Riemann-Stieltjes integral boundary conditions. Krasnosel'skii proposed a theorem in 1960, which has been known as Krasnosel'skii's fixed-point theorem. This paper will use this theorem to derive two significant conclusions regarding the problem to be discussed. It is worth noting that, unlike other problems, the equation studied in this paper has a nonlinear term f that includes the first-order derivative of the unknown function.

Keywords: p-Laplacian; Riemann-Stieltjes integral boundary conditions; cone; positive solution; fixed point theorem.

DOI: 10.1504/IJDSDE.2024.144886

International Journal of Dynamical Systems and Differential Equations, 2024 Vol.13 No.4, pp.393 - 411

Received: 29 Dec 2023
Accepted: 08 Aug 2024
Published online: 06 Mar 2025 *