The method of upper and lower solutions and interval method for first order differential equations (original) (raw)

This paper explores an innovative approach to solving first order differential equations using the method of upper and lower solutions alongside an interval method. Key results demonstrate the existence and uniqueness of solutions for defined nonlinear problems without the monotonicity requirement. Through the application of integral operators and the utilization of specific assumptions, the research establishes rigorous frameworks for both linear and nonlinear equations, contributing to advancements in differential equation methodologies.