The First Application of the Monotone Iterative Technique in Nonlocal Differential Equations With Convolution Coefficients

ABSTRACT At present, in all literature on nonlocal differential equations with convolution coefficients, the fixed point method is adopted, and conditions like convexity, concavity, and growth requirements were involved in. By the first use of the monotone iterative method, we obtain positive minimal and maximal solutions for nonlocal differential equations with convolution coefficients. We do not require that the composite function term in the convolution coefficients have an explicit expression, and we make no assumptions about it other than continuity. Through a specific comparison from six aspects, we conclude that the requirements for the nonlinear term in this article are clearly weaker than those in some existing literature.