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

Abstract

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.

Keywords

• Coupled system
• Lower and upper solutions
• Degree theory