Causal difference equations with upper and lower solutions in the reverse order

Abstract

Abstract This paper is devoted to studying the existence conditions for difference equations involving causal operators in the presence of upper and lower solutions in the reverse order. To this end, we prove some new comparison theorems and develop the upper and lower solutions method. Our results improve and extend some relevant results in difference equations. Two examples are given to illustrate the obtained results.

Keywords

• Upper and lower solutions method
• Causal operators
• Extremal solutions
• Coupled extremal quasi-solutions