Upper and lower solutions method for a class of second-order coupled systems

作者：Zelong Yu, Zhanbing Bai, Suiming Shang · 发表于：Boundary Value Problems · 年份：2024 · DOI：10.1186/s13661-024-01837-3 · 被引用次数：5 · 研究领域：Numerical methods for differential equations、Fractional Differential Equations Solutions、Differential Equations and Numerical Methods

Abstract This paper provides a class of upper and lower solution definitions for second-order coupled systems by transforming the fourth-order differential equation into a second-order differential system. Then, by constructing a homotopy parameter and utilizing the maximum principle, we propose an upper and lower solutions method for studying a class of second-order coupled systems with Dirichlet boundary conditions and obtain an existence result.